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"The female characters in his films reflected the same qualities over and over again", Roger Ebert wrote in 1996 "They were blonde. They were icy and remote. They were imprisoned in costumes that subtly combined fashion with fetishism. They mesmerised the men, who often had physical or psychological handicaps. Sooner or later, every Hitchcock woman was humiliated."
The victims in The Lodger are all blondes. In The 39 Steps, Madeleine Carroll is put in handcuffs. Ingrid Bergman, whom Hitchcock directed three times Spellbound, Notorious, and Under Capricorn, is dark blonde. In Rear Window, Lisa Grace Kelly risks her life by breaking into Lars Thorwald's apartment. In To Catch a Thief, Francie also Kelly offers to help a man she believes is a burglar. In Vertigo and North by Northwest respectively, Kim Novak and Eva Marie Saint play the blonde heroines. In Psycho, Janet Leigh's character steals 40,000 and is murdered by Norman Bates, a reclusive psychopath. Tippi Hedren, a blonde, appears to be the focus of the |
attacks in The Birds. In Marnie, the title character, again played by Hedren, is a thief. In Topaz, French actresses Dany Robin as Stafford's wife and Claude Jade as Stafford's daughter are blonde heroines, the mistress was played by brunette Karin Dor. Hitchcock's last blonde heroine was Barbara Harris as a phony psychic turned amateur sleuth in Family Plot 1976, his final film. In the same film, the diamond smuggler played by Karen Black wears a long blonde wig in several scenes.
His films often feature characters struggling in their relationships with their mothers, such as Norman Bates in Psycho. In North by Northwest, Roger Thornhill Cary Grant is an innocent man ridiculed by his mother for insisting that shadowy, murderous men are after him. In The Birds, the Rod Taylor character, an innocent man, finds his world under attack by vicious birds, and struggles to free himself from a clinging mother Jessica Tandy. The killer in Frenzy has a loathing of women but idolises his mother. The villain Bruno in S |
trangers on a Train hates his father, but has an incredibly close relationship with his mother played by Marion Lorne. Sebastian Claude Rains in Notorious has a clearly conflicting relationship with his mother, who is rightly suspicious of his new bride, Alicia Huberman Ingrid Bergman.
Relationship with actors
Hitchcock became known for having remarked that "actors should be treated like cattle". During the filming of Mr. Mrs. Smith 1941, Carole Lombard brought three cows onto the set wearing the name tags of Lombard, Robert Montgomery, and Gene Raymond, the stars of the film, to surprise him. In an episode of The Dick Cavett Show, originally broadcast on 8 June 1972, Dick Cavett stated as fact that Hitchcock had once called actors cattle. Hitchcock responded by saying that, at one time, he had been accused of calling actors cattle. "I said that I would never say such an unfeeling, rude thing about actors at all. What I probably said, was that all actors should be treated like cattle...In a nice way of co |
urse." He then described Carole Lombard's joke, with a smile.
Hitchcock believed that actors should concentrate on their performances and leave work on script and character to the directors and screenwriters. He told Bryan Forbes in 1967 "I remember discussing with a method actor how he was taught and so forth. He said, 'We're taught using improvisation. We are given an idea and then we are turned loose to develop in any way we want to.' I said, 'That's not acting. That's writing.' "
Recalling their experiences on Lifeboat for Charles Chandler, author of It's Only a Movie Alfred Hitchcock A Personal Biography, Walter Slezak said that Hitchcock "knew more about how to help an actor than any director I ever worked with", and Hume Cronyn dismissed the idea that Hitchcock was not concerned with his actors as "utterly fallacious", describing at length the process of rehearsing and filming Lifeboat.
Critics observed that, despite his reputation as a man who disliked actors, actors who worked with him often gave |
brilliant performances. He used the same actors in many of his films; Cary Grant and James Stewart both worked with Hitchcock four times, and Ingrid Bergman and Grace Kelly three. James Mason said that Hitchcock regarded actors as "animated props". For Hitchcock, the actors were part of the film's setting. He told Franois Truffaut "The chief requisite for an actor is the ability to do nothing well, which is by no means as easy as it sounds. He should be willing to be used and wholly integrated into the picture by the director and the camera. He must allow the camera to determine the proper emphasis and the most effective dramatic highlights."
Writing, storyboards and production
Hitchcock planned his scripts in detail with his writers. In Writing with Hitchcock 2001, Steven DeRosa noted that Hitchcock supervised them through every draft, asking that they tell the story visually. Hitchcock told Roger Ebert in 1969
Hitchcock's films were extensively storyboarded to the finest detail. He was reported to have ne |
ver even bothered looking through the viewfinder, since he did not need to, although in publicity photos he was shown doing so. He also used this as an excuse to never have to change his films from his initial vision. If a studio asked him to change a film, he would claim that it was already shot in a single way, and that there were no alternative takes to consider.
This view of Hitchcock as a director who relied more on preproduction than on the actual production itself has been challenged by Bill Krohn, the American correspondent of French film magazine Cahiers du cinma, in his book Hitchcock at Work. After investigating script revisions, notes to other production personnel written by or to Hitchcock, and other production material, Krohn observed that Hitchcock's work often deviated from how the screenplay was written or how the film was originally envisioned. He noted that the myth of storyboards in relation to Hitchcock, often regurgitated by generations of commentators on his films, was to a great degre |
e perpetuated by Hitchcock himself or the publicity arm of the studios. For example, the celebrated cropspraying sequence of North by Northwest was not storyboarded at all. After the scene was filmed, the publicity department asked Hitchcock to make storyboards to promote the film, and Hitchcock in turn hired an artist to match the scenes in detail.
Even when storyboards were made, scenes that were shot differed from them significantly. Krohn's analysis of the production of Hitchcock classics like Notorious reveals that Hitchcock was flexible enough to change a film's conception during its production. Another example Krohn notes is the American remake of The Man Who Knew Too Much, whose shooting schedule commenced without a finished script and moreover went over schedule, something that, as Krohn notes, was not an uncommon occurrence on many of Hitchcock's films, including Strangers on a Train and Topaz. While Hitchcock did do a great deal of preparation for all his films, he was fully cognisant that the act |
ual filmmaking process often deviated from the bestlaid plans and was flexible to adapt to the changes and needs of production as his films were not free from the normal hassles faced and common routines used during many other film productions.
Krohn's work also sheds light on Hitchcock's practice of generally shooting in chronological order, which he notes sent many films over budget and over schedule and, more importantly, differed from the standard operating procedure of Hollywood in the Studio System Era. Equally important is Hitchcock's tendency to shoot alternative takes of scenes. This differed from coverage in that the films were not necessarily shot from varying angles so as to give the editor options to shape the film how they chose often under the producer's aegis. Rather they represented Hitchcock's tendency to give himself options in the editing room, where he would provide advice to his editors after viewing a rough cut of the work.
According to Krohn, this and a great deal of other informatio |
n revealed through his research of Hitchcock's personal papers, script revisions and the like refute the notion of Hitchcock as a director who was always in control of his films, whose vision of his films did not change during production, which Krohn notes has remained the central longstanding myth of Alfred Hitchcock. Both his fastidiousness and attention to detail also found their way into each film poster for his films. Hitchcock preferred to work with the best talent of his dayfilm poster designers such as Bill Gold and Saul Basswho would produce posters that accurately represented his films.
Legacy
Awards and honours
Hitchcock was inducted into the Hollywood Walk of Fame on 8 February 1960 with two stars one for television and a second for his motion pictures. In 1978, John Russell Taylor described him as "the most universally recognizable person in the world" and "a straightforward middleclass Englishman who just happened to be an artistic genius". In 2002, MovieMaker named him the most influential d |
irector of all time, and a 2007 The Daily Telegraph critics' poll ranked him Britain's greatest director. David Gritten, the newspaper's film critic, wrote "Unquestionably the greatest filmmaker to emerge from these islands, Hitchcock did more than any director to shape modern cinema, which would be utterly different without him. His flair was for narrative, cruelly withholding crucial information from his characters and from us and engaging the emotions of the audience like no one else." In 1992, the Sight Sound Critics' Poll ranked Hitchcock at No. 4 in its list of "Top 10 Directors" of all time. In 2002, Hitchcock was ranked 2nd in the critics' top ten poll and 5th in the directors' top ten poll in the list of The Greatest Directors of All Time compiled by the Sight Sound magazine. Hitchcock was voted the "Greatest Director of 20th Century" in a poll conducted by Japanese film magazine kinema Junpo. In 1996, Entertainment Weekly ranked Hitchcock at No. 1 in its "50 Greatest Directors" list. Hitchcock was |
ranked at No. 2 on Empire magazine's "Top 40 Greatest Directors of AllTime" list in 2005. In 2007, Total Film magazine ranked Hitchcock at No. 1 on its "100 Greatest Film Directors Ever" list.
He won two Golden Globes, eight Laurel Awards, and five lifetime achievement awards, including the first BAFTA Academy Fellowship Award and, in 1979, an AFI Life Achievement Award. He was nominated five times for an Academy Award for Best Director. Rebecca, nominated for 11 Oscars, won the Academy Award for Best Picture of 1940; another Hitchcock film, Foreign Correspondent, was also nominated that year. By 2021, nine of his films had been selected for preservation by the US National Film Registry Rebecca 1940; inducted 2018, Shadow of a Doubt 1943; inducted 1991, Notorious 1946; inducted 2006, Strangers on a Train 1951; inducted 2021, Rear Window 1954; inducted 1997, Vertigo 1958; inducted 1989, North by Northwest 1959; inducted 1995, Psycho 1960; inducted 1992, and The Birds 1963; inducted 2016.
In 2012, Hitchcock |
was selected by artist Sir Peter Blake, author of the Beatles' Sgt. Pepper's Lonely Hearts Club Band album cover, to appear in a new version of the cover, along with other British cultural figures, and he was featured that year in a BBC Radio 4 series, The New Elizabethans, as someone "whose actions during the reign of Elizabeth II have had a significant impact on lives in these islands and given the age its character". In June 2013 nine restored versions of Hitchcock's early silent films, including The Pleasure Garden 1925, were shown at the Brooklyn Academy of Music's Harvey Theatre; known as "The Hitchcock 9", the travelling tribute was organised by the British Film Institute.
Archives
The Alfred Hitchcock Collection is housed at the Academy Film Archive in Hollywood, California. It includes home movies, 16mm film shot on the set of Blackmail 1929 and Frenzy 1972, and the earliest known colour footage of Hitchcock. The Academy Film Archive has preserved many of his home movies. The Alfred Hitchcock Papers |
are housed at the Academy's Margaret Herrick Library. The David O. Selznick and the Ernest Lehman collections housed at the Harry Ransom Humanities Research Center in Austin, Texas, contain material related to Hitchcock's work on the production of The Paradine Case, Rebecca, Spellbound, North by Northwest and Family Plot.
Hitchcock portrayals
Anthony Hopkins in Hitchcock 2012
Toby Jones in The Girl 2012
Roger AshtonGriffiths in Grace of Monaco 2014
Filmography
Films
Silent films
Sound films
See also
Alfred Hitchcock's unrealized projects
List of Alfred Hitchcock cameo appearances
List of film director and actor collaborations
Notes and sources
Notes
References
Works cited
Biographies chronological
Miscellaneous
Further reading
Articles
Hitchcock's Style at the BFI's Screenonline
Books
Deflem, Mathieu. 2016. "Alfred Hitchcock Visions of Guilt and Innocence." pp. 203227 in Framing Law and Crime An Interdisciplinary Anthology, edited by Caroline Joan S. Picart, M |
ichael Hviid Jacobsen, and Cecil Greek. Latham, MD; Madison, NJ Rowman Littlefield; Fairleigh Dickinson University Press.
Slavoj iek et al.Everything You Always Wanted to Know About Lacan But Were Afraid to Ask Hitchcock, London and New York, Verso, 2nd edition 2010
External links
1899 births
1980 deaths
20thcentury screenwriters
20thcentury English businesspeople
20thcentury English people
AFI Life Achievement Award recipients
American people of Irish descent
Articles containing video clips
BAFTA fellows
British Army personnel of World War I
Cecil B. DeMille Award Golden Globe winners
Deaths from kidney failure
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r film directors
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Anacondas or water boas are a group of large snakes of the genus Eunectes. They are found in tropical South America. Four species are currently recognized.
Description
Although the name applies to a group of snakes, it is often used to refer only to one species, in particular, the common or green anaconda Eunectes murinus, which is the largest snake in the world by weight, and the second longest.
Etymology
The South American names anacauchoa and anacaona were suggested in an account by Peter Martyr d'Anghiera, but the idea of a South American origin was questioned by Henry Walter Bates who, in his travels in South America, failed to find any similar name in use. The word anaconda is derived from the name of a snake from Ceylon Sri Lanka that John Ray described in Latin in his Synopsis Methodica Animalium 1693 as serpens indicus bubalinus anacandaia zeylonibus, ides bubalorum aliorumque jumentorum membra conterens. Ray used a catalogue of snakes from the Leyden museum supplied by Dr. Tancred Robinson, but th |
e description of its habit was based on Andreas Cleyer who in 1684 described a gigantic snake that crushed large animals by coiling around their bodies and crushing their bones. Henry Yule in his HobsonJobson notes that the word became more popular due to a piece of fiction published in 1768 in the Scots Magazine by a certain R. Edwin. Edwin described a 'tiger' being crushed to death by an anaconda, when there actually never were any tigers in Sri Lanka. Yule and Frank Wall noted that the snake was in fact a python and suggested a Tamil origin anaikondra meaning elephant killer. A Sinhalese origin was also suggested by Donald Ferguson who pointed out that the word Henakandaya hena lightninglarge and kanda stemtrunk was used in Sri Lanka for the small whip snake Ahaetulla pulverulenta and somehow got misapplied to the python before myths were created.
The name commonly used for the anaconda in Brazil is sucuri, sucuriju or sucuriuba.
Species and other uses of the term "anaconda"
The term "anaconda" has been |
used to refer to
Any member of the genus Eunectes, a group of large, aquatic snakes found in South America
Eunectes murinus, the green anaconda the largest species, found east of the Andes in Colombia, Venezuela, the Guianas, Ecuador, Peru, Bolivia, Brazil and Trinidad and Tobago
Eunectes notaeus, the yellow anaconda a small species, found in eastern Bolivia, southern Brazil, Paraguay, and northeastern Argentina
Eunectes deschauenseei, the darklyspotted anaconda a rare species, found in northeastern Brazil and coastal French Guiana
Eunectes beniensis, the Bolivian anaconda the most recently defined species, found in the Departments of Beni and Pando in Bolivia
The term was previously applied imprecisely, indicating any large snake that constricts its prey, though this usage is now archaic.
"Anaconda" is also used as a metaphor for an action aimed at constricting and suffocating an opponent for example, the Anaconda Plan proposed at the beginning of the American Civil War, in which the Union Army |
was to effectively "suffocate" the Confederacy. Another example is the anaconda choke in the martial art Brazilian jiujitsu, which is performed by wrapping your arms under the opponent's neck and through the armpit, and grasping the biceps of the opposing arm, when caught in this move, you will lose consciousness if you do not tap out.
See also
South American jaguar, a competitor or predator
Notes
References
Eunectes
Snake common names |
Altaic ; also called Transeurasian is a sprachbund i.e. a linguistic area and proposed language family that would include the Turkic, Mongolic and Tungusic language families and possibly also the Japonic and Koreanic languages. Speakers of these languages are currently scattered over most of Asia north of 35 N and in some eastern parts of Europe, extending in longitude from Turkey to Japan. The group is named after the Altai mountain range in the center of Asia.
The hypothetical language family has long been rejected by most comparative linguists, although it continues to be supported by a small but stable scholarly minority.
The Altaic family was first proposed in the 18th century. It was widely accepted until the 1960s and is still listed in many encyclopedias and handbooks. Since the 1950s, many comparative linguists have rejected the proposal, after supposed cognates were found not to be valid, hypothesized sound shifts were not found, and Turkic and Mongolic languages were found to be converging rather |
than diverging over the centuries. Opponents of the theory proposed that the similarities are due to mutual linguistic influences between the groups concerned. Modern supporters of Altaic acknowledge that many shared features are the result of contact and convergence and thus cannot be taken as evidence for a genetic relationship, but they nevertheless argue that a core of existing correspondences goes back to a common ancestor.
The original hypothesis unified only the Turkic, Mongolian, and Tungusic groups. Later proposals to include the Korean and Japanese languages into a "MacroAltaic" family have always been controversial. The original proposal was sometimes called "MicroAltaic" by retronymy. Most proponents of Altaic continue to support the inclusion of Korean. A common ancestral ProtoAltaic language for the "Macro" family has been tentatively reconstructed by Sergei Starostin and others. Some proposals also included Ainuic but this is not widely accepted even among Altaicists themselves.
MicroAltaic i |
ncludes about 66 living languages, to which MacroAltaic would add Korean, Jeju, Japanese, and the Ryukyuan languages, for a total of about 74 depending on what is considered a language and what is considered a dialect. These numbers do not include earlier states of languages, such as Middle Mongol, Old Korean, or Old Japanese.
Earliest attestations of the languages
The earliest known texts in a Turkic language are the Orkhon inscriptions, 720735 AD. They were deciphered in 1893 by the Danish linguist Vilhelm Thomsen in a scholarly race with his rival, the GermanRussian linguist Wilhelm Radloff. However, Radloff was the first to publish the inscriptions.
The first Tungusic language to be attested is Jurchen, the language of the ancestors of the Manchus. A writing system for it was devised in 1119 AD and an inscription using this system is known from 1185 see List of Jurchen inscriptions.
The earliest Mongolic language of which we have written evidence is known as Middle Mongol. It is first attested by an in |
scription dated to 1224 or 1225 AD, the Stele of Yisngge, and by the Secret History of the Mongols, written in 1228 see Mongolic languages. The earliest ParaMongolic text is the Memorial for Yel Yanning, written in the Khitan large script and dated to 986 AD. However, the Inscription of His Tolgoi, discovered in 1975 and analysed as being in an early form of Mongolic, has been dated to 604620 AD. The Bugut inscription dates back to 584 AD.
Japanese is first attested in the form of names contained in a few short inscriptions in Classical Chinese from the 5th century AD, such as found on the Inariyama Sword. The first substantial text in Japanese, however, is the Kojiki, which dates from 712 AD. It is followed by the Nihon shoki, completed in 720, and then by the Man'ysh, which dates from c. 771785, but includes material that is from about 400 years earlier.
The most important text for the study of early Korean is the Hyangga, a collection of 25 poems, of which some go back to the Three Kingdoms period 57 BC6 |
68 AD, but are preserved in an orthography that only goes back to the 9th century AD. Korean is copiously attested from the mid15th century on in the phonetically precise Hangul system of writing.
History of the Altaic family concept
Origins
The earliest known reference to a unified language group of Turkic, Mongolic and Tungusic languages is from the 1692 work of Nicolaes Witsen which may be based on a 1661 work of Abu alGhazi Bahadur Genealogy of the Turks.
A proposed grouping of the Turkic, Mongolic, and Tungusic languages was published in 1730 by Philip Johan von Strahlenberg, a Swedish officer who traveled in the eastern Russian Empire while a prisoner of war after the Great Northern War. However, he may not have intended to imply a closer relationship among those languages.
UraloAltaic hypothesis
In 1844, the Finnish philologist Matthias Castrn proposed a broader grouping, that later came to be called the UralAltaic family, which included Turkic, Mongolian, and ManchuTungus Tungusic as an "Altaic" b |
ranch, and also the FinnoUgric and Samoyedic languages as the "Uralic" branch though Castrn himself used the terms "Tataric" and "Chudic". The name "Altaic" referred to the Altai Mountains in EastCentral Asia, which are approximately the center of the geographic range of the three main families. The name "Uralic" referred to the Ural Mountains.
While the UralAltaic family hypothesis can still be found in some encyclopedias, atlases, and similar general references, after the 1960s it has been heavily criticized. Even linguists who accept the basic Altaic family, like Sergei Starostin, completely discard the inclusion of the "Uralic" branch.
Korean and Japanese languages
In 1857, the Austrian scholar Anton Boller suggested adding Japanese to the UralAltaic family.
In the 1920s, G.J. Ramstedt and E.D. Polivanov advocated the inclusion of Korean. Decades later, in his 1952 book, Ramstedt rejected the UralAltaic hypothesis but again included Korean in Altaic, an inclusion followed by most leading Altaicists sup |
porters of the theory to date. His book contained the first comprehensive attempt to identify regular correspondences among the sound systems within the Altaic language families.
In 1960, Nicholas Poppe published what was in effect a heavily revised version of Ramstedt's volume on phonology that has since set the standard in Altaic studies. Poppe considered the issue of the relationship of Korean to TurkicMongolicTungusic not settled. In his view, there were three possibilities 1 Korean did not belong with the other three genealogically, but had been influenced by an Altaic substratum; 2 Korean was related to the other three at the same level they were related to each other; 3 Korean had split off from the other three before they underwent a series of characteristic changes.
Roy Andrew Miller's 1971 book Japanese and the Other Altaic Languages convinced most Altaicists that Japanese also belonged to Altaic. Since then, the "MacroAltaic" has been generally assumed to include Turkic, Mongolic, Tungusic, Korea |
n, and Japanese.
In 1990, Unger advocated a family consisting of Tungusic, Korean, and Japonic languages, but not Turkic or Mongolic.
However, many linguists dispute the alleged affinities of Korean and Japanese to the other three groups. Some authors instead tried to connect Japanese to the Austronesian languages.
In 2017, Martine Robbeets proposed that Japanese and possibly Korean originated as a hybrid language. She proposed that the ancestral home of the Turkic, Mongolic, and Tungusic languages was somewhere in northwestern Manchuria. A group of those protoAltaic "Transeurasian" speakers would have migrated south into the modern Liaoning province, where they would have been mostly assimilated by an agricultural community with an Austronesianlike language. The fusion of the two languages would have resulted in protoJapanese and protoKorean.
In a typological study that does not directly evaluate the validity of the Altaic hypothesis, Yurayong and Szeto 2020 discuss for Koreanic and Japonic the stages of |
convergence to the Altaic typological model and subsequent divergence from that model, which resulted in the present typological similarity between Koreanic and Japonic. They state that both are "still so different from the Core Altaic languages that we can even speak of an independent JapaneseKorean type of grammar. Given also that there is neither a strong proof of common ProtoAltaic lexical items nor solid regular sound correspondences but, rather, only lexical and structural borrowings between languages of the Altaic typology, our results indirectly speak in favour of a PaleoAsiatic origin of the Japonic and Koreanic languages."
The Ainu language
In 1962, John C. Street proposed an alternative classification, with TurkicMongolicTungusic in one grouping and KoreanJapaneseAinu in another, joined in what he designated as the "North Asiatic" family. The inclusion of Ainu was adopted also by James Patrie in 1982.
The TurkicMongolicTungusic and KoreanJapaneseAinu groupings were also posited in 20002002 by Jo |
seph Greenberg. However, he treated them as independent members of a larger family, which he termed Eurasiatic.
The inclusion of Ainu is not widely accepted by Altaicists. In fact, no convincing genealogical relationship between Ainu and any other language family has been demonstrated, and it is generally regarded as a language isolate.
Early criticism and rejection
Starting in the late 1950s, some linguists became increasingly critical of even the minimal Altaic family hypothesis, disputing the alleged evidence of genetic connection between Turkic, Mongolic and Tungusic languages.
Among the earlier critics were Gerard Clauson 1956, Gerhard Doerfer 1963, and Alexander Shcherbak. They claimed that the words and features shared by Turkic, Mongolic, and Tungusic languages were for the most part borrowings and that the rest could be attributed to chance resemblances. In 1988, Doerfer again rejected all the genetic claims over these major groups.
Modern controversy
A major continuing supporter of the Altaic hy |
pothesis has been Sergei Starostin, who published a comparative lexical analysis of the Altaic languages in 1991. He concluded that the analysis supported the Altaic grouping, although it was "older than most other language families in Eurasia, such as IndoEuropean or FinnoUgric, and this is the reason why the modern Altaic languages preserve few common elements".
In 1991 and again in 1996, Roy Miller defended the Altaic hypothesis and claimed that the criticisms of Clauson and Doerfer apply exclusively to the lexical correspondences, whereas the most pressing evidence for the theory is the similarities in verbal morphology.
In 2003, Claus Schnig published a critical overview of the history of the Altaic hypothesis up to that time, siding with the earlier criticisms of Clauson, Doerfer, and Shcherbak.
In 2003, Starostin, Anna Dybo and Oleg Mudrak published the Etymological Dictionary of the Altaic Languages, which expanded the 1991 lexical lists and added other phonological and grammatical arguments.
Star |
ostin's book was criticized by Stefan Georg in 2004 and 2005, and by Alexander Vovin in 2005.
Other defenses of the theory, in response to the criticisms of Georg and Vovin, were published by Starostin in 2005, Blaek in 2006, Robbeets in 2007, and Dybo and G. Starostin in 2008
In 2010, Lars Johanson echoed Miller's 1996 rebuttal to the critics, and called for a muting of the polemic.
List of supporters and critics of the Altaic hypothesis
The list below comprises linguists who have worked specifically on the Altaic problem since the publication of the first volume of Ramstedt's Einfhrung in 1952. The dates given are those of works concerning Altaic. For supporters of the theory, the version of Altaic they favor is given at the end of the entry, if other than the prevailing one of TurkicMongolicTungusicKoreanJapanese.
Major supporters
Pentti Aalto 1955. TurkicMongolicTungusicKorean.
Anna V. Dybo S. Starostin et al. 2003, A. Dybo and G. Starostin 2008.
Frederik Kortlandt 2010.
Karl H. Menges 1975. Common an |
cestor of Korean, Japanese and traditional Altaic dated back to the 7th or 8th millennium BC 1975 125.
Roy Andrew Miller 1971, 1980, 1986, 1996. Supported the inclusion of Korean and Japanese.
Oleg A. Mudrak S. Starostin et al. 2003.
Nicholas Poppe 1965. TurkicMongolicTungusic and perhaps Korean.
Alexis Manaster Ramer.
Martine Robbeets 2004, 2005, 2007, 2008, 2015 in the form of "Transeurasian".
G. J. Ramstedt 19521957. TurkicMongolicTungusicKorean.
George Starostin A. Dybo and G. Starostin 2008.
Sergei Starostin 1991, S. Starostin et al. 2003.
John C. Street 1962. TurkicMongolicTungusic and KoreanJapaneseAinu, grouped as "North Asiatic".
Talat Tekin 1994. TurkicMongolicTungusicKorean.
Major critics
Gerard Clauson 1956, 1959, 1962.
Gerhard Doerfer 1963, 1966, 1967, 1968, 1972, 1973, 1974, 1975, 1981, 1985, 1988, 1993.
Susumu no 1970, 2000
Juha Janhunen 1992, 1995 tentative support of MongolicTungusic.
Claus Schnig 2003.
Stefan Georg 2004, 2005.
Alexander Vovin 2005, 2010, 2017. Formerly an advocate of Altai |
c 1994, 1995, 1997, 1999, 2000, 2001, now a critic.
Alexander Shcherbak.
Alexander B. M. Stiven 2008, 2010.
Advocates of alternative hypotheses
James Patrie 1982 and Joseph Greenberg 20002002. TurkicMongolicTungusic and KoreanJapaneseAinu, grouped in a common taxon cf. John C. Street 1962, called Eurasiatic by Greenberg.
J. Marshall Unger 1990. TungusicKoreanJapanese "MacroTungusic", with Turkic and Mongolic as separate language families.
Lars Johanson 2010. Agnostic, proponent of a "Transeurasian" verbal morphology not necessarily genealogically linked.
Languages
Tungusic languages
With fewer speakers than Mongolic or Turkic languages, Tungusic languages are distributed across most of Eastern Siberia including the Sakhalin Island, northern Manchuria and extending into some parts of Xinjiang and Mongolia. Some Tungusic languages are extinct or endangered languages as a consequence of language shift to Chinese and Russian. In China, where the Tungusic population is over 10 million, just 46,000 still retai |
n knowledge of their ethnic languages.
Scholars have yet to reach agreement on how to classify the Tungusic languages but two subfamilies have been proposed South Tungusic or Manchu and North Tungusic Tungus. Jurchen now extinct; Da Jin , Manchu critically endangered; Da Qing , Sibe Xibo and other minor languages comprise the Manchu group.
The Northern Tungusic languages can be reclassified even further into the Siberian Tungusic languages Evenki, Lamut, Solon and Negidal and the Lower Amur Tungusic languages Nanai, Ulcha, Orok to name a few.
Significant disagreements remain, not only about the linguistic subclassifications but also some controversy around the Chinese names of some ethnic groups, like the use of Hezhe for the Nanai people.
Mongolic languages
Mongolic languages are spoken in three geographic areas Russia especially Siberia, China and Mongolia. Although Russia and China host significant Mongol populations many of the Mongol people in these countries don't speak their own ethnic language. |
They are usually subclassified into two groups the Western languages Oirat, Kalmyk and related dialects and Eastern languages. The latter group can be further subdivided as follows
Southern Mongol Ordos, Chakhar and Khorchin
Central Mongol Khalkha, Darkhat
Northern Mongol Buriat and dialects, Khamnigan
There are also additional archaic and obscure languages within these groups Moghol Afghanistan, Dagur Manchuria and languages associated with Gansu and Qinghai.
Linguisitically two branches emerge, the Common Mongolic and the KhitanSerbi sometimes called "paraMongolic". Of the latter, only Dagur survives into the present day.
Arguments
For the Altaic grouping
Phonological and grammatical features
The original arguments for grouping the "microAltaic" languages within a UraloAltaic family were based on such shared features as vowel harmony and agglutination.
According to Roy Miller, the most pressing evidence for the theory is the similarities in verbal morphology.
The Etymological Dictionary by Staro |
stin and others 2003 proposes a set of sound change laws that would explain the evolution from ProtoAltaic to the descendant languages. For example, although most of today's Altaic languages have vowel harmony, ProtoAltaic as reconstructed by them lacked it; instead, various vowel assimilations between the first and second syllables of words occurred in Turkic, Mongolic, Tungusic, Korean, and Japonic. They also included a number of grammatical correspondences between the languages.
Shared lexicon
Starostin claimed in 1991 that the members of the proposed Altaic group shared about 1520 of apparent cognates within a 110word SwadeshYakhontov list; in particular, TurkicMongolic 20, TurkicTungusic 18, TurkicKorean 17, MongolicTungusic 22, MongolicKorean 16, and TungusicKorean 21. The 2003 Etymological Dictionary includes a list of 2,800 proposed cognate sets, as well as a few important changes to the reconstruction of ProtoAltaic. The authors tried hard to distinguish loans between Turkic and Mongolic and between |
Mongolic and Tungusic from cognates; and suggest words that occur in Turkic and Tungusic but not in Mongolic. All other combinations between the five branches also occur in the book. It lists 144 items of shared basic vocabulary, including words for such items as 'eye', 'ear', 'neck', 'bone', 'blood', 'water', 'stone', 'sun', and 'two'.
Robbeets and Bouckaert 2018 use Bayesian phylolinguistic methods to argue for the coherence of the "narrow" Altaic languages Turkic, Mongolic, and Tungusic together with Japonic and Koreanic, which they refer to as the Transeurasian languages. Their results include the following phylogenetic tree
Martine Robbeets 2020 argues that early Transeurasian speakers were originally agriculturalists in northeastern China, only becoming pastoralists later on. Some lexical reconstructions of agricultural terms by Robbeets 2020 are listed below.
Abbreviations
PTEA ProtoTranseurasian
PA ProtoAltaic
PTk ProtoTurkic
PMo ProtoMongolic
PTg ProtoTungusic
PJK ProtoJapanoKoreanic
PK Pr |
otoKoreanic
PJ ProtoJaponic
Additional familylevel reconstructions of agricultural vocabulary from Robbeets et al. 2020
ProtoTurkic ek to sprinkle with the hand; sow eke.g. plow
ProtoTurkic tar to cultivate the ground targ what is cultivated; crops, main crop, cultivated land
ProtoTurkic ko to put kon to settle down of animals, to take up residence of people, to be planted of plants konak foxtail millet Setaria italica
ProtoTurkic tg to hit, beat; to pound, crush food in a mortar; to husk, thresh cereals tgi husked millet; husked rice
ProtoTurkic gr broomcorn millet
ProtoTurkic arpa barley Hordeum vulgare' ? ProtoIranian arbus barley
ProtoMongolic amun cereals; broomcorn millet Panicum miliaceum Nugteren 2011 268
ProtoMongolic konag foxtail millet PTk konak foxtail millet Setaria italica
ProtoMongolic budaga cooked cereals; porridge; meal
ProtoMongolic tari to sow, plant Nugteren 2011 51213
ProtoMacroMongolic pre seed; descendants
ProtoTungusic pisike broomcorn millet Panicum miliaceum
|
ProtoTungusic jiya foxtail millet Setaria italica
ProtoTungusic murgi barley Hordeum vulgare
ProtoTungusic se si to plant se si seed, seedling, sin field for cultivation
ProtoTungusic tari to sow, to plant
ProtoKoreanic pisi seed, pihi barnyard millet ProtoTranseurasian PTEA pisii sowNMLZ seed pisike sowRES.NMLZ what is sown, major crop
ProtoKoreanic patk dry field ProtoJapanoKoreanic PJK pata dry field PTEA pata field for cultivation
ProtoKoreanic mutk dry land PJK muta land PTEA mudu uncultivated land
ProtoKoreanic matk garden plot PJK mat plot of land for cultivation
ProtoKoreanic non rice paddy field PJK non field
ProtoKoreanic pap any boiled preparation of cereal; boiled rice
ProtoKoreanic psal hulled of any grain; hulled corn of grain; hulled rice ProtoJaponic wasara early ripening of any grain
ProtoKoreanic ipi pi pye unhusked rice ProtoJaponic ipi eatNMLZ cooked millet, steamed rice
ProtoJaponic nuka rice bran PJ nuka remove.NMLZ
ProtoJaponic mmi hulled rice PJ mmi move.ba |
ck.and.forth.with.forceNMLZ
ProtoJaponic ipi cooked millet, steamed rice ipi eatNMLZ PK meki rice offered to a higher rank meki eatNMLZ what you eat, food ProtoAustronesian kaen eatOBJ.NMLZ
ProtoJaponic wasa ws to be early ripening of crops; an early ripening variety of any crop; earlyripening rice plant
ProtoJaponic usu rice and grain mortar ParaAustronesian lusu rice mortar; cf. ProtoAustronesian lusu rice mortar
ProtoJaponic kmai dehusked rice ParaAustronesian hemay ProtoMacroAustronesian Semay cooked rice; cf. ProtoAustronesian Semay cooked rice
Against the grouping
Weakness of lexical and typological data
According to G. Clauson 1956, G. Doerfer 1963, and A. Shcherbak 1963, many of the typological features of the supposed Altaic languages, particularly agglutinative strongly suffixing morphology and subjectobjectverb SOV word order, often occur together in languages.
Those critics also argued that the words and features shared by Turkic, Mongolic, and Tungusic languages were for the most p |
art borrowings and that the rest could be attributed to chance resemblances. They noted that there was little vocabulary shared by Turkic and Tungusic languages, though more shared with Mongolic languages. They reasoned that, if all three families had a common ancestor, we should expect losses to happen at random, and not only at the geographical margins of the family; and that the observed pattern is consistent with borrowing.
According to C. Schnig 2003, after accounting for areal effects, the shared lexicon that could have a common genetic origin was reduced to a small number of monosyllabic lexical roots, including the personal pronouns and a few other deictic and auxiliary items, whose sharing could be explained in other ways; not the kind of sharing expected in cases of genetic relationship.
The Sprachbund hypothesis
Instead of a common genetic origin, Clauson, Doerfer, and Shcherbak proposed in 19561966 that Turkic, Mongolic, and Tungusic languages form a Sprachbund a set of languages with similariti |
es due to convergence through intensive borrowing and long contact, rather than common origin.
Asya Pereltsvaig further observed in 2011 that, in general, genetically related languages and families tend to diverge over time the earlier forms are more similar than modern forms. However, she claims that an analysis of the earliest written records of Mongolic and Turkic languages shows the opposite, suggesting that they do not share a common traceable ancestor, but rather have become more similar through language contact and areal effects.
Hypothesis about the original homeland
The prehistory of the peoples speaking the "Altaic" languages is largely unknown. Whereas for certain other language families, such as the speakers of IndoEuropean, Uralic, and Austronesian, it is possible to frame substantial hypotheses, in the case of the proposed Altaic family much remains to be done.
Some scholars have hypothesised a possible Uralic and Altaic homeland in the Central Asian steppes.
According to Juha Janhunen, the |
ancestral languages of Turkic, Mongolic, Tungusic, Korean, and Japanese were spoken in a relatively small area comprising presentday North Korea, Southern Manchuria, and Southeastern Mongolia. However Janhunen is sceptical about an affiliation of Japanese to Altaic, while Andrs RnaTas remarked that a relationship between Altaic and Japanese, if it ever existed, must be more remote than the relationship of any two of the IndoEuropean languages. Ramsey stated that "the genetic relationship between Korean and Japanese, if it in fact exists, is probably more complex and distant than we can imagine on the basis of our present state of knowledge".
Supporters of the Altaic hypothesis formerly set the date of the ProtoAltaic language at around 4000 BC, but today at around 5000 BC or 6000 BC. This would make Altaic a language family older than IndoEuropean around 3000 to 4000 BC according to mainstream hypotheses but considerably younger than Afroasiatic c. 10,000 BC or 11,000 to 16,000 BC according to different sou |
rces.
See also
Classification of the Japonic languages
Nostratic languages
PanTuranism
TurcoMongol
UraloSiberian languages
Xiongnu
Comparison of Japanese and Korean
References
Citations
Sources
Aalto, Pentti. 1955. "On the Altaic initial p." Central Asiatic Journal 1, 916.
Anonymous. 2008. title missing. Bulletin of the Society for the Study of the Indigenous Languages of the Americas, 31 March 2008, 264 .
Anthony, David W. 2007. The Horse, the Wheel, and Language. Princeton Princeton University Press.
Boller, Anton. 1857. Nachweis, da das Japanische zum uralaltaischen Stamme gehrt. Wien.
Clauson, Gerard. 1959. "The case for the Altaic theory examined." Akten des vierundzwanzigsten internationalen OrientalistenKongresses, edited by H. Franke. Wiesbaden Deutsche Morgenlndische Gesellschaft, in Komission bei Franz Steiner Verlag.
Clauson, Gerard. 1968. "A lexicostatistical appraisal of the Altaic theory." Central Asiatic Journal 13 123.
Doerfer, Gerhard. 1973. "Lautgesetze und Zufall Betrachtungen zum |
Omnicomparativismus." Innsbrucker Beitrge zur Sprachwissenschaft 10.
Doerfer, Gerhard. 1974. "Ist das Japanische mit den altaischen Sprachen verwandt?" Zeitschrift der Deutschen Morgenlndischen Gesellschaft 114.1.
Doerfer, Gerhard. 1985. MongolicaTungusica. Wiesbaden Otto Harrassowitz.
Georg, Stefan. 1999 2000. "Haupt und Glieder der altaischen Hypothese die Krperteilbezeichnungen im Trkischen, Mongolischen und Tungusischen" 'Head and members of the Altaic hypothesis The bodypart designations in Turkic, Mongolic, and Tungusic'. Uralaltaische Jahrbcher, neue Folge B 16, 143182.
.
Lee, KiMoon and S. Robert Ramsey. 2011. A History of the Korean Language. Cambridge Cambridge University Press.
Menges, Karl. H. 1975. Altajische Studien II. Japanisch und Altajisch. Wiesbaden Franz Steiner Verlag.
Miller, Roy Andrew. 1980. Origins of the Japanese Language Lectures in Japan during the Academic Year 19771978. Seattle University of Washington Press. .
Ramstedt, G.J. 1952. Einfhrung in die altaische Sprachwissenscha |
ft I. Lautlehre, 'Introduction to Altaic Linguistics, Volume 1 Phonology', edited and published by Pentti Aalto. Helsinki SuomalaisUgrilainen Seura.
Ramstedt, G.J. 1957. Einfhrung in die altaische Sprachwissenschaft II. Formenlehre, 'Introduction to Altaic Linguistics, Volume 2 Morphology', edited and published by Pentti Aalto. Helsinki SuomalaisUgrilainen Seura.
Ramstedt, G.J. 1966. Einfhrung in die altaische Sprachwissenschaft III. Register, 'Introduction to Altaic Linguistics, Volume 3 Index', edited and published by Pentti Aalto. Helsinki SuomalaisUgrilainen Seura.
Robbeets, Martine. 2004. "Swadesh 100 on Japanese, Korean and Altaic." Tokyo University Linguistic Papers, TULIP 23, 99118.
Robbeets, Martine. 2005. Is Japanese related to Korean, Tungusic, Mongolic and Turkic? Wiesbaden Otto Harrassowitz.
Strahlenberg, P.J.T. von. 1730. Das nord und ostliche Theil von Europa und Asia.... Stockholm. Reprint 1975. Studia UraloAltaica. Szeged and Amsterdam.
Strahlenberg, P.J.T. von. 1738. Russia, Siberia and Gre |
at Tartary, an Historicogeographical Description of the North and Eastern Parts of Europe and Asia.... Reprint 1970. New York Arno Press. English translation of the previous.
Tekin, Talat. 1994. "Altaic languages." In The Encyclopedia of Language and Linguistics, Vol. 1, edited by R.E. Asher. Oxford and New York Pergamon Press.
Vovin, Alexander. 1993. "About the phonetic value of the Middle Korean grapheme ." Bulletin of the School of Oriental and African Studies 562, 247259.
Vovin, Alexander. 1994. "Genetic affiliation of Japanese and methodology of linguistic comparison." Journal de la Socit finnoougrienne 85, 241256.
Vovin, Alexander. 2001. "Japanese, Korean, and Tungusic evidence for genetic relationship from verbal morphology." Altaic Affinities Proceedings of the 40th Meeting of PIAC, Provo, Utah, 1997, edited by David B. Honey and David C. Wright, 83202. Indiana University, Research Institute for Inner Asian Studies.
Vovin, Alexander. 2010. KoreoJaponica A ReEvaluation of a Common Genetic Origin. Un |
iversity of Hawaii Press.
Whitney Coolidge, Jennifer. 2005. Southern Turkmenistan in the Neolithic A Petrographic Case Study. Oxbow Books.
Further reading
Greenberg, Joseph H. 1997. "Does Altaic exist?" In Irn Hegedus, Peter A. Michalove, and Alexis Manaster Ramer editors, IndoEuropean, Nostratic and Beyond A Festschrift for Vitaly V. Shevoroshkin, Washington, DC Institute for the Study of Man, 1997, 8893. Reprinted in Joseph H. Greenberg, Genetic Linguistics, Oxford Oxford University Press, 2005, 325330.
Hahn, Reinhard F. 1994. LINGUIST List 5.908, 18 August 1994.
Janhune, Juha. 1995. "Prolegomena to a Comparative Analysis of Mongolic and Tungusic". Proceedings of the 38th Permanent International Altaistic Conference PIAC, 209218. Wiesbaden Harrassowitz.
Johanson, Lars. 1999. "Cognates and copies in Altaic verb derivation." Language and Literature Japanese and the Other Altaic Languages Studies in Honour of Roy Andrew Miller on His 75th Birthday, edited by Karl H. Menges and Nelly Naumann, 113. Wiesbaden |
Otto Harrassowitz. Also HTML version.
Johanson, Lars. 1999. "Attractiveness and relatedness Notes on Turkic language contacts." Proceedings of the Twentyfifth Annual Meeting of the Berkeley Linguistics Society Special Session on Caucasian, Dravidian, and Turkic Linguistics, edited by Jeff Good and Alan C.L. Yu, 8794. Berkeley Berkeley Linguistics Society.
Johanson, Lars. 2002. Structural Factors in Turkic Language Contacts, translated by Vanessa Karam. Richmond, Surrey Curzon Press.
Kortlandt, Frederik. 1993. "The origin of the Japanese and Korean accent systems." Acta Linguistica Hafniensia 26, 5765.
Robbeets, Martine. 2004. "Belief or argument? The classification of the Japanese language." Eurasia Newsletter 8. Graduate School of Letters, Kyoto University.
Ruhlen, Merritt. 1987. A Guide to the World's Languages. Stanford University Press.
Sinor, Denis. 1990. Essays in Comparative Altaic Linguistics. Bloomington Indiana University, Research Institute for Inner Asian Studies. .
Vovin, Alexander. 2009. Jap |
anese, Korean, and other 'nonAltaic' languages. Central Asiatic Journal 53 1 105147.
External links
Altaic at the Linguist List MultiTree Project not functional as of 2014 Genealogical trees attributed to Ramstedt 1957, Miller 1971, and Poppe 1982
Swadesh vocabulary lists for Altaic languages from Wiktionary's Swadeshlist appendix
Monumenta altaica Altaic linguistics website, maintained by Ilya Gruntov
Altaic Etymological Dictionary, database version by Sergei A. Starostin, Anna V. Dybo, and Oleg A. Mudrak does not include introductory chapters
LINGUIST List 5.911 defense of Altaic by Alexis Manaster Ramer 1994
LINGUIST List 5.926 1. Remarks by Alexander Vovin. 2. Clarification by J. Marshall Unger. 1994
Agglutinative languages
Central Asia
Proposed language families |
Austrian German , Austrian Standard German ASG, Standard Austrian German , or Austrian High German , is the variety of Standard German written and spoken in Austria. It has the highest sociolinguistic prestige locally, as it is the variation used in the media and for other formal situations. In less formal situations, Austrians tend to use forms closer to or identical with the Bavarian and Alemannic dialects, traditionally spoken but rarely written in Austria.
History
German in Austria Austria German has its beginning in the mid18th century, when empress Maria Theresa and her son Joseph II introduced compulsory schooling in 1774 and several reforms of administration in their multilingual Habsburg empire. At the time, the written standard was Oberdeutsche Schreibsprache Upper German written language, which was highly influenced by the Bavarian and Alemannic dialects of Austria. Another option was to create a new standard based on the Southern German dialects, as proposed by the linguist Johann Siegmund Popo |
witsch. Instead they decided for pragmatic reasons to adopt the already standardized chancellery language of Saxony Schsische Kanzleisprache or Meiner Kanzleideutsch, which was based on the administrative language of the nonAustrian area of Meien and Dresden.
Austria High German Hochdeutsch in sterreich, not to be confused with the Bavarian Austria German dialects has the same geographic origin as the Swiss High German Schweizer Hochdeutsch, not to be confused with the Alemannic Swiss German dialects.
The process of introducing the new written standard was led by Joseph von Sonnenfels.
Since 1951 the standardized form of Austrian German for official texts and schools has been defined by the Austrian Dictionary , published under the authority of the Austrian Federal Ministry of Education, Arts and Culture.
General situation of German
As German is a pluricentric language, Austrian German is one among several varieties of German. Much like the relationship between British English and American English, the Ger |
man varieties differ in minor respects e.g., spelling, word usage and grammar but are recognizably equivalent and largely mutually intelligible.
Standard Austrian German in Austria
The official Austrian dictionary, das sterreichische Wrterbuch, prescribes grammatical and spelling rules defining the official language.
Austrian delegates participated in the international working group that drafted the German spelling reform of 1996several conferences leading up to the reform were hosted in Vienna at the invitation of the Austrian federal governmentand adopted it as a signatory, along with Germany, Switzerland, and Liechtenstein, of an international memorandum of understanding signed in Vienna in 1996.
The eszett or "sharp s" is used in Austria, as in Germany but unlike in Switzerland.
Because of the German language's pluricentric nature, German dialects in Austria should not be confused with the variety of Standard Austrian German spoken by most Austrians, which is distinct from that of Germany or Switzer |
land.
Distinctions in vocabulary persist, for example, in culinary terms, where communication with Germans is frequently difficult, and administrative and legal language, which is due to Austria's exclusion from the development of a German nationstate in the late 19th century and its manifold particular traditions. A comprehensive collection of AustrianGerman legal, administrative and economic terms is offered in Markhardt, Heidemarie Wrterbuch der sterreichischen Rechts, Wirtschafts und Verwaltungsterminologie Peter Lang, 2006.
Former spoken standard
Until 1918, the spoken standard in Austria was the , a sociolect spoken by the imperial Habsburg family and the nobility of AustriaHungary. The dialect was similar to Viennese German and other eastern dialects of German spoken in Austria, but was slightly nasalized.
Special written forms
For many years, Austria had a special form of the language for official government documents. This form is known as , or "Austrian chancellery language". It is a very traditi |
onal form of the language, probably derived from medieval deeds and documents, and has a very complex structure and vocabulary generally reserved for such documents. For most speakers even native speakers, this form of the language is generally difficult to understand, as it contains many highly specialised terms for diplomatic, internal, official, and military matters. There are no regional variations, because this special written form has mainly been used by a government that has now for centuries been based in Vienna.
is now used less and less, thanks to various administrative reforms that reduced the number of traditional civil servants . As a result, Standard Austrian German is replacing it in government and administrative texts.
European Union
When Austria became a member of the European Union, 23 foodrelated terms were listed in its accession agreement as having the same legal status as the equivalent terms used in Germany,
for example, the words for "potato", "tomato", and "Brussels sprouts". Exam |
ples in "Vocabulary"
Austrian German is the only variety of a pluricentric language recognized under international law or EU primary law.
Grammar
Verbs
In Austria, as in the Germanspeaking parts of Switzerland and in southern Germany, verbs that express a state tend to use as the auxiliary verb in the perfect, as well as verbs of movement. Verbs which fall into this category include sitzen to sit, liegen to lie and, in parts of Carinthia, schlafen to sleep. Therefore, the perfect of these verbs would be ich bin gesessen, ich bin gelegen and ich bin geschlafen respectively.
In Germany, the words stehen to stand and gestehen to confess are identical in the present perfect habe gestanden. The Austrian variant avoids this potential ambiguity bin gestanden from stehen, "to stand"; and habe gestanden from gestehen, "to confess", e.g. "der Verbrecher ist vor dem Richter gestanden und hat gestanden".
In addition, the preterite simple past is very rarely used in Austria, especially in the spoken language, with th |
e exception of some modal verbs i.e. ich sollte, ich wollte.
Vocabulary
There are many official terms that differ in Austrian German from their usage in most parts of Germany. Words used in Austria are Jnner January rather than Januar, Feber seldom, February along with Februar, heuer this year along with dieses Jahr, Stiege stairs along with Treppen, Rauchfang chimney instead of Schornstein, many administrative, legal and political terms, and many food terms, including the following
There are, however, some false friends between the two regional varieties
Kasten wardrobe along with or instead of Schrank and, similarly, Eiskasten along with Khlschrank, fridge, as opposed to Kiste box instead of Kasten. Kiste in Germany means both "box" and "chest".
Sessel chair instead of Stuhl. Sessel means "" in Germany and Stuhl means "stool faeces" in both varieties.
Dialects
Classification
Dialects of the AustroBavarian group, which also comprises dialects from Bavaria
Central AustroBavarian along the main rivers Isa |
r and Danube, spoken in the northern parts of the State of Salzburg, Upper Austria, Lower Austria, and northern Burgenland
Viennese German
Southern AustroBavarian in Tyrol, South Tyrol, Carinthia, Styria, and the southern parts of Salzburg and Burgenland
Vorarlbergerisch, spoken in Vorarlberg, is a High Alemannic dialect.
Regional accents
In addition to the standard variety, in everyday life most Austrians speak one of a number of Upper German dialects.
While strong forms of the various dialects are not fully mutually intelligible to northern Germans, communication is much easier in Bavaria, especially rural areas, where the Bavarian dialect still predominates as the mother tongue. The Central AustroBavarian dialects are more intelligible to speakers of Standard German than the Southern AustroBavarian dialects of Tyrol.
Viennese, the AustroBavarian dialect of Vienna, is seen for many in Germany as quintessentially Austrian. The people of Graz, the capital of Styria, speak yet another dialect which is not v |
ery Styrian and more easily understood by people from other parts of Austria than other Styrian dialects, for example from western Styria.
Simple words in the various dialects are very similar, but pronunciation is distinct for each and, after listening to a few spoken words, it may be possible for an Austrian to realise which dialect is being spoken. However, in regard to the dialects of the deeper valleys of the Tyrol, other Tyroleans are often unable to understand them. Speakers from the different states of Austria can easily be distinguished from each other by their particular accents probably more so than Bavarians, those of Carinthia, Styria, Vienna, Upper Austria, and the Tyrol being very characteristic. Speakers from those regions, even those speaking Standard German, can usually be easily identified by their accent, even by an untrained listener.
Several of the dialects have been influenced by contact with nonGermanic linguistic groups, such as the dialect of Carinthia, where, in the past, many spe |
akers were bilingual and, in the southeastern portions of the state, many still are even today with Slovene, and the dialect of Vienna, which has been influenced by immigration during the AustroHungarian period, particularly from what is today Czechia. The German dialects of South Tyrol have been influenced by local Romance languages, particularly noticeable with the many loanwords from Italian and Ladin.
The geographic borderlines between the different accents isoglosses coincide strongly with the borders of the states and also with the border with Bavaria, with Bavarians having a markedly different rhythm of speech in spite of the linguistic similarities.
References
Notes
Citations
Works cited
Further reading
Die deutsche Sprache in Deutschland, sterreich und der Schweiz Das Problem der nationalen Varietten. de Gruyter, BerlinNew York 1995.
Ammon, Ulrich Hans Bickel, Jakob Ebner u. a. Variantenwrterbuch des Deutschen. Die Standardsprache in sterreich, der Schweiz und Deutschland sowie in Liechtenste |
in, Luxemburg, Ostbelgien und Sdtirol. BerlinNew York 2004, .
Dollinger, Stefan sterreichisches Deutsch oder Deutsch in sterreich? Identitten im 21. Jahrhundert. New Academic Press, 2021. ISBN 9783990360231.
Grzega, Joachim Deutschlndisch und sterreichisches Deutsch Mehr Unterschiede als nur in Wortschatz und Aussprache. In Joachim Grzega Sprachwissenschaft ohne Fachchinesisch. Shaker, Aachen 2001, S. 726. .
Grzega, Joachim "On the Description of National Varieties Examples from German and Austrian German and English and American English". In Linguistik Online 7 2000.
Grzega, Joachim "Nonchalance als Merkmal des sterreichischen Deutsch". In Muttersprache 113 2003 242254.
Muhr, Rudolf Schrodt, Richard sterreichisches Deutsch und andere nationale Varietten plurizentrischer Sprachen in Europa. Wien, 1997
Muhr, RudolfSchrodt, RichardWiesinger, Peter eds. sterreichisches Deutsch Linguistische, sozialpsychologische und sprachpolitische Aspekte einer nationalen Variante des Deutschen. Wien, 1995.
Pohl, Heinz Diete |
r sterreichische Identitt und sterreichisches Deutsch aus dem Krntner Jahrbuch fr Politik 1999Wiesinger, Peter Die deutsche Sprache in sterreich. Eine Einfhrung, In Wiesinger Hg. Das sterreichische Deutsch. Schriften zur deutschen Sprache. Band 12.'' Wien, Kln, Graz, 1988, Verlag, Bhlau
External links
Austrian German German Dictionary
Das sterreichische Volkswrterbuch
Bavarian language
German dialects
German
National varieties of German |
In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that a Cartesian product of a collection of nonempty sets is nonempty. Informally put, the axiom of choice says that given any collection of bins, each containing at least one object, it is possible to make a selection of exactly one object from each bin, even if the collection is infinite. Formally, it states that for every indexed family of nonempty sets there exists an indexed family of elements such that for every . The axiom of choice was formulated in 1904 by Ernst Zermelo in order to formalize his proof of the wellordering theorem.
In many cases, such a selection can be made without invoking the axiom of choice; this is in particular the case if the number of sets is finite, or if a selection rule is available some distinguishing property that happens to hold for exactly one element in each set. An illustrative example is sets picked from the natural numbers. From such sets, one may always select the |
smallest number, e.g. given the sets 4, 5, 6, 10, 12, 1, 400, 617, 8000 the set containing each smallest element is 4, 10, 1. In this case, "select the smallest number" is a choice function. Even if infinitely many sets were collected from the natural numbers, it will always be possible to choose the smallest element from each set to produce a set. That is, the choice function provides the set of chosen elements. However, no choice function is known for the collection of all nonempty subsets of the real numbers if there are nonconstructible reals. In that case, the axiom of choice must be invoked.
Bertrand Russell coined an analogy for any even infinite collection of pairs of shoes, one can pick out the left shoe from each pair to obtain an appropriate selection; this makes it possible to directly define a choice function. For an infinite collection of pairs of socks assumed to have no distinguishing features, there is no obvious way to make a function that selects one sock from each pair, without invoking |
the axiom of choice.
Although originally controversial, the axiom of choice is now used without reservation by most mathematicians, and it is included in the standard form of axiomatic set theory, ZermeloFraenkel set theory with the axiom of choice ZFC. One motivation for this use is that a number of generally accepted mathematical results, such as Tychonoff's theorem, require the axiom of choice for their proofs. Contemporary set theorists also study axioms that are not compatible with the axiom of choice, such as the axiom of determinacy. The axiom of choice is avoided in some varieties of constructive mathematics, although there are varieties of constructive mathematics in which the axiom of choice is embraced.
Statement
A choice function also called selector or selection is a function f, defined on a collection X of nonempty sets, such that for every set A in X, fA is an element of A. With this concept, the axiom can be stated
Formally, this may be expressed as follows
Thus, the negation of the axiom |
of choice states that there exists a collection of nonempty sets that has no choice function. , so where is negation.
Each choice function on a collection X of nonempty sets is an element of the Cartesian product of the sets in X. This is not the most general situation of a Cartesian product of a family of sets, where a given set can occur more than once as a factor; however, one can focus on elements of such a product that select the same element every time a given set appears as factor, and such elements correspond to an element of the Cartesian product of all distinct sets in the family. The axiom of choice asserts the existence of such elements; it is therefore equivalent to
Given any family of nonempty sets, their Cartesian product is a nonempty set.
Nomenclature ZF, AC, and ZFC
In this article and other discussions of the Axiom of Choice the following abbreviations are common
AC the Axiom of Choice.
ZF ZermeloFraenkel set theory omitting the Axiom of Choice.
ZFC ZermeloFraenkel set theory, exten |
ded to include the Axiom of Choice.
Variants
There are many other equivalent statements of the axiom of choice. These are equivalent in the sense that, in the presence of other basic axioms of set theory, they imply the axiom of choice and are implied by it.
One variation avoids the use of choice functions by, in effect, replacing each choice function with its range.
Given any set X of pairwise disjoint nonempty sets, there exists at least one set C that contains exactly one element in common with each of the sets in X.
This guarantees for any partition of a set X the existence of a subset C of X containing exactly one element from each part of the partition.
Another equivalent axiom only considers collections X that are essentially powersets of other sets
For any set A, the power set of A with the empty set removed has a choice function.
Authors who use this formulation often speak of the choice function on A, but this is a slightly different notion of choice function. Its domain is the power set of A wi |
th the empty set removed, and so makes sense for any set A, whereas with the definition used elsewhere in this article, the domain of a choice function on a collection of sets is that collection, and so only makes sense for sets of sets. With this alternate notion of choice function, the axiom of choice can be compactly stated as
Every set has a choice function.
which is equivalent to
For any set A there is a function f such that for any nonempty subset B of A, fB lies in B.
The negation of the axiom can thus be expressed as
There is a set A such that for all functions f on the set of nonempty subsets of A, there is a B such that fB does not lie in B.
Restriction to finite sets
The statement of the axiom of choice does not specify whether the collection of nonempty sets is finite or infinite, and thus implies that every finite collection of nonempty sets has a choice function. However, that particular case is a theorem of the ZermeloFraenkel set theory without the axiom of choice ZF; it is easily proved by |
mathematical induction. In the even simpler case of a collection of one set, a choice function just corresponds to an element, so this instance of the axiom of choice says that every nonempty set has an element; this holds trivially. The axiom of choice can be seen as asserting the generalization of this property, already evident for finite collections, to arbitrary collections.
Usage
Until the late 19th century, the axiom of choice was often used implicitly, although it had not yet been formally stated. For example, after having established that the set X contains only nonempty sets, a mathematician might have said "let Fs be one of the members of s for all s in X" to define a function F. In general, it is impossible to prove that F exists without the axiom of choice, but this seems to have gone unnoticed until Zermelo.
Not every situation requires the axiom of choice. For finite sets X, the axiom of choice follows from the other axioms of set theory. In that case, it is equivalent to saying that if we ha |
ve several a finite number of boxes, each containing at least one item, then we can choose exactly one item from each box. Clearly, we can do this We start at the first box, choose an item; go to the second box, choose an item; and so on. The number of boxes is finite, so eventually, our choice procedure comes to an end. The result is an explicit choice function a function that takes the first box to the first element we chose, the second box to the second element we chose, and so on. A formal proof for all finite sets would use the principle of mathematical induction to prove "for every natural number k, every family of k nonempty sets has a choice function." This method cannot, however, be used to show that every countable family of nonempty sets has a choice function, as is asserted by the axiom of countable choice. If the method is applied to an infinite sequence Xi i of nonempty sets, a function is obtained at each finite stage, but there is no stage at which a choice function for the entire family is c |
onstructed, and no "limiting" choice function can be constructed, in general, in ZF without the axiom of choice.
Examples
The nature of the individual nonempty sets in the collection may make it possible to avoid the axiom of choice even for certain infinite collections. For example, suppose that each member of the collection X is a nonempty subset of the natural numbers. Every such subset has a smallest element, so to specify our choice function we can simply say that it maps each set to the least element of that set. This gives us a definite choice of an element from each set, and makes it unnecessary to apply the axiom of choice.
The difficulty appears when there is no natural choice of elements from each set. If we cannot make explicit choices, how do we know that our set exists? For example, suppose that X is the set of all nonempty subsets of the real numbers. First we might try to proceed as if X were finite. If we try to choose an element from each set, then, because X is infinite, our choice pr |
ocedure will never come to an end, and consequently, we shall never be able to produce a choice function for all of X. Next we might try specifying the least element from each set. But some subsets of the real numbers do not have least elements. For example, the open interval 0,1 does not have a least element if x is in 0,1, then so is x2, and x2 is always strictly smaller than x. So this attempt also fails.
Additionally, consider for instance the unit circle S, and the action on S by a group G consisting of all rational rotations. Namely, these are rotations by angles which are rational multiples of . Here G is countable while S is uncountable. Hence S breaks up into uncountably many orbits under G. Using the axiom of choice, we could pick a single point from each orbit, obtaining an uncountable subset X of S with the property that all of its translates by G are disjoint from X. The set of those translates partitions the circle into a countable collection of disjoint sets, which are all pairwise congruen |
t. Since X is not measurable for any rotationinvariant countably additive finite measure on S, finding an algorithm to select a point in each orbit requires the axiom of choice. See nonmeasurable set for more details.
The reason that we are able to choose least elements from subsets of the natural numbers is the fact that the natural numbers are wellordered every nonempty subset of the natural numbers has a unique least element under the natural ordering. One might say, "Even though the usual ordering of the real numbers does not work, it may be possible to find a different ordering of the real numbers which is a wellordering. Then our choice function can choose the least element of every set under our unusual ordering." The problem then becomes that of constructing a wellordering, which turns out to require the axiom of choice for its existence; every set can be wellordered if and only if the axiom of choice holds.
Criticism and acceptance
A proof requiring the axiom of choice may establish the existenc |
e of an object without explicitly defining the object in the language of set theory. For example, while the axiom of choice implies that there is a wellordering of the real numbers, there are models of set theory with the axiom of choice in which no wellordering of the reals is definable. Similarly, although a subset of the real numbers that is not Lebesgue measurable can be proved to exist using the axiom of choice, it is consistent that no such set is definable.
The axiom of choice proves the existence of these intangibles objects that are proved to exist, but which cannot be explicitly constructed, which may conflict with some philosophical principles. Because there is no canonical wellordering of all sets, a construction that relies on a wellordering may not produce a canonical result, even if a canonical result is desired as is often the case in category theory. This has been used as an argument against the use of the axiom of choice.
Another argument against the axiom of choice is that it implies the |
existence of objects that may seem counterintuitive. One example is the BanachTarski paradox which says that it is possible to decompose the 3dimensional solid unit ball into finitely many pieces and, using only rotations and translations, reassemble the pieces into two solid balls each with the same volume as the original. The pieces in this decomposition, constructed using the axiom of choice, are nonmeasurable sets.
Despite these seemingly paradoxical facts, most mathematicians accept the axiom of choice as a valid principle for proving new results in mathematics. The debate is interesting enough, however, that it is considered of note when a theorem in ZFC ZF plus AC is logically equivalent with just the ZF axioms to the axiom of choice, and mathematicians look for results that require the axiom of choice to be false, though this type of deduction is less common than the type which requires the axiom of choice to be true.
It is possible to prove many theorems using neither the axiom of choice nor its ne |
gation; such statements will be true in any model of ZF, regardless of the truth or falsity of the axiom of choice in that particular model. The restriction to ZF renders any claim that relies on either the axiom of choice or its negation unprovable. For example, the BanachTarski paradox is neither provable nor disprovable from ZF alone it is impossible to construct the required decomposition of the unit ball in ZF, but also impossible to prove there is no such decomposition. Similarly, all the statements listed below which require choice or some weaker version thereof for their proof are unprovable in ZF, but since each is provable in ZF plus the axiom of choice, there are models of ZF in which each statement is true. Statements such as the BanachTarski paradox can be rephrased as conditional statements, for example, "If AC holds, then the decomposition in the BanachTarski paradox exists." Such conditional statements are provable in ZF when the original statements are provable from ZF and the axiom of choice |
.
In constructive mathematics
As discussed above, in ZFC, the axiom of choice is able to provide "nonconstructive proofs" in which the existence of an object is proved although no explicit example is constructed. ZFC, however, is still formalized in classical logic. The axiom of choice has also been thoroughly studied in the context of constructive mathematics, where nonclassical logic is employed. The status of the axiom of choice varies between different varieties of constructive mathematics.
In MartinLf type theory and higherorder Heyting arithmetic, the appropriate statement of the axiom of choice is depending on approach included as an axiom or provable as a theorem. Errett Bishop argued that the axiom of choice was constructively acceptable, saying
In constructive set theory, however, Diaconescu's theorem shows that the axiom of choice implies the law of excluded middle unlike in MartinLf type theory, where it does not. Thus the axiom of choice is not generally available in constructive set theory. |
A cause for this difference is that the axiom of choice in type theory does not have the extensionality properties that the axiom of choice in constructive set theory does.
Some results in constructive set theory use the axiom of countable choice or the axiom of dependent choice, which do not imply the law of the excluded middle in constructive set theory. Although the axiom of countable choice in particular is commonly used in constructive mathematics, its use has also been questioned.
Independence
In 1938, Kurt Gdel showed that the negation of the axiom of choice is not a theorem of ZF by constructing an inner model the constructible universe which satisfies ZFC and thus showing that ZFC is consistent if ZF itself is consistent. In 1963, Paul Cohen employed the technique of forcing, developed for this purpose, to show that, assuming ZF is consistent, the axiom of choice itself is not a theorem of ZF. He did this by constructing a much more complex model which satisfies ZFC ZF with the negation of AC ad |
ded as axiom and thus showing that ZFC is consistent.
Together these results establish that the axiom of choice is logically independent of ZF. The assumption that ZF is consistent is harmless because adding another axiom to an already inconsistent system cannot make the situation worse. Because of independence, the decision whether to use the axiom of choice or its negation in a proof cannot be made by appeal to other axioms of set theory. The decision must be made on other grounds.
One argument given in favor of using the axiom of choice is that it is convenient to use it because it allows one to prove some simplifying propositions that otherwise could not be proved. Many theorems which are provable using choice are of an elegant general character every ideal in a ring is contained in a maximal ideal, every vector space has a basis, and every product of compact spaces is compact. Without the axiom of choice, these theorems may not hold for mathematical objects of large cardinality.
The proof of the indep |
endence result also shows that a wide class of mathematical statements, including all statements that can be phrased in the language of Peano arithmetic, are provable in ZF if and only if they are provable in ZFC. Statements in this class include the statement that P NP, the Riemann hypothesis, and many other unsolved mathematical problems. When one attempts to solve problems in this class, it makes no difference whether ZF or ZFC is employed if the only question is the existence of a proof. It is possible, however, that there is a shorter proof of a theorem from ZFC than from ZF.
The axiom of choice is not the only significant statement which is independent of ZF. For example, the generalized continuum hypothesis GCH is not only independent of ZF, but also independent of ZFC. However, ZF plus GCH implies AC, making GCH a strictly stronger claim than AC, even though they are both independent of ZF.
Stronger axioms
The axiom of constructibility and the generalized continuum hypothesis each imply the axiom |
of choice and so are strictly stronger than it. In class theories such as Von NeumannBernaysGdel set theory and MorseKelley set theory, there is an axiom called the axiom of global choice that is stronger than the axiom of choice for sets because it also applies to proper classes. The axiom of global choice follows from the axiom of limitation of size. Tarski's axiom, which is used in TarskiGrothendieck set theory and states in the vernacular that every set belongs to Grothendieck universe, is stronger than the axiom of choice.
Equivalents
There are important statements that, assuming the axioms of ZF but neither AC nor AC, are equivalent to the axiom of choice. The most important among them are Zorn's lemma and the wellordering theorem. In fact, Zermelo initially introduced the axiom of choice in order to formalize his proof of the wellordering theorem.
Set theory
Wellordering theorem Every set can be wellordered. Consequently, every cardinal has an initial ordinal.
Tarski's theorem about choice For ever |
y infinite set A, there is a bijective map between the sets A and AA.
Trichotomy If two sets are given, then either they have the same cardinality, or one has a smaller cardinality than the other.
Given two nonempty sets, one has a surjection to the other.
The Cartesian product of any family of nonempty sets is nonempty.
Knig's theorem Colloquially, the sum of a sequence of cardinals is strictly less than the product of a sequence of larger cardinals. The reason for the term "colloquially" is that the sum or product of a "sequence" of cardinals cannot be defined without some aspect of the axiom of choice.
Every surjective function has a right inverse.
Order theory
Zorn's lemma Every nonempty partially ordered set in which every chain i.e., totally ordered subset has an upper bound contains at least one maximal element.
Hausdorff maximal principle In any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset. The restricted principle "Every partially ordered set h |
as a maximal totally ordered subset" is also equivalent to AC over ZF.
Tukey's lemma Every nonempty collection of finite character has a maximal element with respect to inclusion.
Antichain principle Every partially ordered set has a maximal antichain.
Abstract algebra
Every vector space has a basis.
Krull's theorem Every unital ring other than the trivial ring contains a maximal ideal.
For every nonempty set S there is a binary operation defined on S that gives it a group structure. A cancellative binary operation is enough, see group structure and the axiom of choice.
Every free abelian group is projective.
Baer's criterion Every divisible abelian group is injective.
Every set is a projective object in the category Set of sets.
Functional analysis
The closed unit ball of the dual of a normed vector space over the reals has an extreme point.
Pointset topology
Tychonoff's theorem Every product of compact topological spaces is compact.
In the product topology, the closure of a product of subsets is equal to t |
he product of the closures.
Mathematical logic
If S is a set of sentences of firstorder logic and B is a consistent subset of S, then B is included in a set that is maximal among consistent subsets of S. The special case where S is the set of all firstorder sentences in a given signature is weaker, equivalent to the Boolean prime ideal theorem; see the section "Weaker forms" below.
Graph theory
Every connected graph has a spanning tree.
Category theory
There are several results in category theory which invoke the axiom of choice for their proof. These results might be weaker than, equivalent to, or stronger than the axiom of choice, depending on the strength of the technical foundations. For example, if one defines categories in terms of sets, that is, as sets of objects and morphisms usually called a small category, or even locally small categories, whose homobjects are sets, then there is no category of all sets, and so it is difficult for a categorytheoretic formulation to apply to all sets. On the ot |
her hand, other foundational descriptions of category theory are considerably stronger, and an identical categorytheoretic statement of choice may be stronger than the standard formulation, la class theory, mentioned above.
Examples of categorytheoretic statements which require choice include
Every small category has a skeleton.
If two small categories are weakly equivalent, then they are equivalent.
Every continuous functor on a smallcomplete category which satisfies the appropriate solution set condition has a leftadjoint the Freyd adjoint functor theorem.
Weaker forms
There are several weaker statements that are not equivalent to the axiom of choice, but are closely related. One example is the axiom of dependent choice DC. A still weaker example is the axiom of countable choice AC or CC, which states that a choice function exists for any countable set of nonempty sets. These axioms are sufficient for many proofs in elementary mathematical analysis, and are consistent with some principles, such as the Le |
besgue measurability of all sets of reals, that are disprovable from the full axiom of choice.
Other choice axioms weaker than axiom of choice include the Boolean prime ideal theorem and the axiom of uniformization. The former is equivalent in ZF to Tarski's 1930 ultrafilter lemma every filter is a subset of some ultrafilter.
Results requiring AC or weaker forms but weaker than it
One of the most interesting aspects of the axiom of choice is the large number of places in mathematics that it shows up. Here are some statements that require the axiom of choice in the sense that they are not provable from ZF but are provable from ZFC ZF plus AC. Equivalently, these statements are true in all models of ZFC but false in some models of ZF.
Set theory
The ultrafilter lemma with ZF can be used to prove the Axiom of choice for finite sets Given and a collection of nonempty sets, their product is not empty.
Any union of countably many countable sets is itself countable because it is necessary to choose a partic |
ular ordering for each of the countably many sets.
If the set A is infinite, then there exists an injection from the natural numbers N to A see Dedekind infinite.
Eight definitions of a finite set are equivalent.
Every infinite game in which is a Borel subset of Baire space is determined.
Measure theory
The Vitali theorem on the existence of nonmeasurable sets which states that there is a subset of the real numbers that is not Lebesgue measurable.
The Hausdorff paradox.
The BanachTarski paradox.
Algebra
Every field has an algebraic closure.
Every field extension has a transcendence basis.
Stone's representation theorem for Boolean algebras needs the Boolean prime ideal theorem.
The NielsenSchreier theorem, that every subgroup of a free group is free.
The additive groups of R and C are isomorphic.
Functional analysis
The HahnBanach theorem in functional analysis, allowing the extension of linear functionals
The theorem that every Hilbert space has an orthonormal basis.
The BanachAlaoglu theorem about compact |
ness of sets of functionals.
The Baire category theorem about complete metric spaces, and its consequences, such as the open mapping theorem and the closed graph theorem.
On every infinitedimensional topological vector space there is a discontinuous linear map.
General topology
A uniform space is compact if and only if it is complete and totally bounded.
Every Tychonoff space has a Stoneech compactification.
Mathematical logic
Gdel's completeness theorem for firstorder logic every consistent set of firstorder sentences has a completion. That is, every consistent set of firstorder sentences can be extended to a maximal consistent set.
The compactness theorem If is a set of firstorder or alternatively, zeroorder sentences such that every finite subset of has a model, then has a model.
Possibly equivalent implications of AC
There are several historically important settheoretic statements implied by AC whose equivalence to AC is open. The partition principle, which was formulated before AC itself, was cited b |
y Zermelo as a justification for believing AC. In 1906, Russell declared PP to be equivalent, but whether the partition principle implies AC is still the oldest open problem in set theory, and the equivalences of the other statements are similarly hard old open problems. In every known model of ZF where choice fails, these statements fail too, but it is unknown if they can hold without choice.
Set theory
Partition principle if there is a surjection from A to B, there is an injection from B to A. Equivalently, every partition P of a set S is less than or equal to S in size.
Converse SchrderBernstein theorem if two sets have surjections to each other, they are equinumerous.
Weak partition principle A partition of a set S cannot be strictly larger than S. If WPP holds, this already implies the existence of a nonmeasurable set. Each of the previous three statements is implied by the preceding one, but it is unknown if any of these implications can be reversed.
There is no infinite decreasing sequence of cardinal |
s. The equivalence was conjectured by Schoenflies in 1905.
Abstract algebra
Hahn embedding theorem Every ordered abelian group G orderembeds as a subgroup of the additive group endowed with a lexicographical order, where is the set of Archimedean equivalence classes of G. This equivalence was conjectured by Hahn in 1907.
Stronger forms of the negation of AC
If we abbreviate by BP the claim that every set of real numbers has the property of Baire, then BP is stronger than AC, which asserts the nonexistence of any choice function on perhaps only a single set of nonempty sets. Strengthened negations may be compatible with weakened forms of AC. For example, ZF DC BP is consistent, if ZF is.
It is also consistent with ZF DC that every set of reals is Lebesgue measurable; however, this consistency result, due to Robert M. Solovay, cannot be proved in ZFC itself, but requires a mild large cardinal assumption the existence of an inaccessible cardinal. The much stronger axiom of determinacy, or AD, implies th |
at every set of reals is Lebesgue measurable, has the property of Baire, and has the perfect set property all three of these results are refuted by AC itself. ZF DC AD is consistent provided that a sufficiently strong large cardinal axiom is consistent the existence of infinitely many Woodin cardinals.
Quine's system of axiomatic set theory, "New Foundations" NF, takes its name from the title "New Foundations for Mathematical Logic" of the 1937 article which introduced it. In the NF axiomatic system, the axiom of choice can be disproved.
Statements consistent with the negation of AC
There are models of ZermeloFraenkel set theory in which the axiom of choice is false. We shall abbreviate "ZermeloFraenkel set theory plus the negation of the axiom of choice" by ZFC. For certain models of ZFC, it is possible to prove the negation of some standard facts.
Any model of ZFC is also a model of ZF, so for each of the following statements, there exists a model of ZF in which that statement is true.
In some model, |
there is a set that can be partitioned into strictly more equivalence classes than the original set has elements, and a function whose domain is strictly smaller than its range. In fact, this is the case in all known models.
There is a function f from the real numbers to the real numbers such that f is not continuous at a, but f is sequentially continuous at a, i.e., for any sequence xn converging to a, limn fxnfa.
In some model, there is an infinite set of real numbers without a countably infinite subset.
In some model, the real numbers are a countable union of countable sets. This does not imply that the real numbers are countable As pointed out above, to show that a countable union of countable sets is itself countable requires the Axiom of countable choice.
In some model, there is a field with no algebraic closure.
In all models of ZFC there is a vector space with no basis.
In some model, there is a vector space with two bases of different cardinalities.
In some model there is a free complete boolean alg |
ebra on countably many generators.
In some model there is a set that cannot be linearly ordered.
There exists a model of ZFC in which every set in Rn is measurable. Thus it is possible to exclude counterintuitive results like the BanachTarski paradox which are provable in ZFC. Furthermore, this is possible whilst assuming the Axiom of dependent choice, which is weaker than AC but sufficient to develop most of real analysis.
In all models of ZFC, the generalized continuum hypothesis does not hold.
For proofs, see .
Additionally, by imposing definability conditions on sets in the sense of descriptive set theory one can often prove restricted versions of the axiom of choice from axioms incompatible with general choice. This appears, for example, in the Moschovakis coding lemma.
Axiom of choice in type theory
In type theory, a different kind of statement is known as the axiom of choice. This form begins with two types, and , and a relation R between objects of type and objects of type . The axiom of cho |
ice states that if for each x of type there exists a y of type such that Rx,y, then there is a function f from objects of type to objects of type such that Rx,fx holds for all x of type
Unlike in set theory, the axiom of choice in type theory is typically stated as an axiom scheme, in which R varies over all formulas or over all formulas of a particular logical form.
Quotes
This is a joke although the three are all mathematically equivalent, many mathematicians find the axiom of choice to be intuitive, the wellordering principle to be counterintuitive, and Zorn's lemma to be too complex for any intuition.
The observation here is that one can define a function to select from an infinite number of pairs of shoes by stating for example, to choose a left shoe. Without the axiom of choice, one cannot assert that such a function exists for pairs of socks, because left and right socks are presumably indistinguishable.
PolishAmerican mathematician Jan Mycielski relates this anecdote in a 2006 article in th |
e Notices of the AMS.
This quote comes from the famous April Fools' Day article in the computer recreations column of the Scientific American, April 1989.
Notes
References
Per MartinLf, "100 years of Zermelo's axiom of choice What was the problem with it?", in Logicism, Intuitionism, and Formalism What Has Become of Them?, Sten Lindstrm, Erik Palmgren, Krister Segerberg, and Viggo StoltenbergHansen, editors 2008.
, available as a Dover Publications reprint, 2013, .
Herman Rubin, Jean E. Rubin Equivalents of the axiom of choice. North Holland, 1963. Reissued by Elsevier, April 1970. .
Herman Rubin, Jean E. Rubin Equivalents of the Axiom of Choice II. North HollandElsevier, July 1985, .
George Tourlakis, Lectures in Logic and Set Theory. Vol. II Set Theory, Cambridge University Press, 2003.
Ernst Zermelo, "Untersuchungen ber die Grundlagen der Mengenlehre I," Mathematische Annalen 65 1908 pp. 26181. PDF download via digizeitschriften.de
Translated in Jean van Heijenoort, 2002. Fr |
om Frege to Gdel A Source Book in Mathematical Logic, 18791931. New edition. Harvard University Press.
1904. "Proof that every set can be wellordered," 13941.
1908. "Investigations in the foundations of set theory I," 199215.
External links
Axiom of Choice entry in the Springer Encyclopedia of Mathematics.
Axiom of Choice and Its Equivalents entry at ProvenMath. Includes formal statement of the Axiom of Choice, Hausdorff's Maximal Principle, Zorn's Lemma and formal proofs of their equivalence down to the finest detail.
Consequences of the Axiom of Choice, based on the book by Paul Howard and Jean Rubin.
. |
Attila , ; , frequently called Attila the Hun, was the ruler of the Huns from 434 until his death in March 453. He was also the leader of a tribal empire consisting of Huns, Ostrogoths, Alans and Bulgars, among others, in Central and Eastern Europe. He is also considered one of the most powerful rulers in world history.
During his reign, he was one of the most feared enemies of the Western and Eastern Roman Empires. He crossed the Danube twice and plundered the Balkans, but was unable to take Constantinople. His unsuccessful campaign in Persia was followed in 441 by an invasion of the Eastern Roman Byzantine Empire, the success of which emboldened Attila to invade the West. He also attempted to conquer Roman Gaul modern France, crossing the Rhine in 451 and marching as far as Aurelianum Orlans before being stopped in the Battle of the Catalaunian Plains.
He subsequently invaded Italy, devastating the northern provinces, but was unable to take Rome. He planned for further campaigns against the Romans, but di |
ed in 453. After Attila's death, his close adviser, Ardaric of the Gepids, led a Germanic revolt against Hunnic rule, after which the Hunnic Empire quickly collapsed. Attila would live on as a character in Germanic heroic legend.
Appearance and character
There is no surviving firsthand account of Attila's appearance, but there is a possible secondhand source provided by Jordanes, who cites a description given by Priscus.
Some scholars have suggested that this description is typically East Asian, because it has all the combined features that fit the physical type of people from Eastern Asia, and Attila's ancestors may have come from there. Other historians also believed that the same descriptions were also evident on some Scythian people.
Etymology
Many scholars have argued that the name Attila derives from East Germanic origin; Attila is formed from the Gothic or Gepidic noun atta, "father", by means of the diminutive suffix ila, meaning "little father", compare Wulfila from wulfs "wolf" and ila, i.e. |
"little wolf". The Gothic etymology was first proposed by Jacob and Wilhelm Grimm in the early 19th century. MaenchenHelfen notes that this derivation of the name "offers neither phonetic nor semantic difficulties", and Gerhard Doerfer notes that the name is simply correct Gothic. Alexander Savelyev and Choongwon Jeong 2020 similarly state that Attila's name "must have been Gothic in origin." The name has sometimes been interpreted as a Germanization of a name of Hunnic origin.
Other scholars have argued for a Turkic origin of the name. Omeljan Pritsak considered Attla a composite titlename which derived from Turkic es great, old, and til sea, ocean, and the suffix a. The stressed back syllabic til assimilated the front member es, so it became as. It is a nominative, in form of attl etsl es tl with the meaning "the oceanic, universal ruler". J. J. Mikkola connected it with Turkic t name, fame.
As another Turkic possibility, H. Althof 1902 considered it was related to Turkish atli horseman, cavalier, or T |
urkish at horse and dil tongue. MaenchenHelfen argues that Pritsak's derivation is "ingenious but for many reasons unacceptable", while dismissing Mikkola's as "too farfetched to be taken seriously". M. Sndal similarly notes that none of these proposals has achieved wide acceptance.
Criticizing the proposals of finding Turkic or other etymologies for Attila, Doerfer notes that King George VI of the United Kingdom had a name of Greek origin, and Sleyman the Magnificent had a name of Arabic origin, yet that does not make them Greeks or Arabs it is therefore plausible that Attila would have a name not of Hunnic origin. Historian Hyun Jin Kim, however, has argued that the Turkic etymology is "more probable".
M. Sndal, in a paper that rejects the Germanic derivation but notes the problems with the existing proposed Turkic etymologies, argues that Attila's name could have originated from TurkicMongolian at, adyyagta gelding, warhorse and Turkish atli horseman, cavalier, meaning "possessor of geldings, provider of |
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