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3701 | encyclopedias, atlases, and similar general references, it has generally been abandoned by linguists. For instance, it was characterized by Sergei Starostin as "an idea now completely discarded". In 1857, the Austrian scholar Anton Boller suggested adding Japanese to the Ural–Altaic family. In the 1920s, G.J. Ramstedt and E.D. Polivanov advocated the inclusion of Korean. However, Ramstedt's three-volume, "Einführung in die altaische Sprachwissenschaft" ('Introduction to Altaic Linguistics'), published in 1952–1966, rejected the Ural–Altaic hypothesis and again included Korean in Altaic, an inclusion followed by most leading Altaicists to date. The first volume of his work, "Lautlehre" ('Phonology'), contained the first comprehensive | "Altaic languages" | [
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3702 | 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 Turkic-Mongolic-Tungusic 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 | "Altaic languages" | [
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3703 | split off from the other three before they underwent a series of characteristic changes. Micro-Altaic includes about 66 living languages, to which Macro-Altaic would add Korean, Japanese and the Ryukyuan languages, for a total of about 74 (depending on what is considered a language and what is considered a dialect). (The numbers do not include earlier states of languages, such as Middle Mongol, Old Korean or Old Japanese.) Roy Andrew Miller's 1971 book "Japanese and the Other Altaic Languages" convinced most Altaicists that Japanese also belonged to Altaic. Since then, the standard set of languages included in Macro-Altaic has been | "Altaic languages" | [
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3704 | Turkic, Mongolic, Tungusic, Korean, and Japanese. An alternative classification, though one with much less currency among Altaicists, was proposed by John C. Street (1962), according to which Turkic-Mongolic-Tungusic forms one grouping and Korean-Japanese-Ainu another, the two being linked in a common family that Street designated as "North Asiatic". The same schema was adopted by James Patrie (1982) in the context of an attempt to classify the Ainu language. The Turkic-Mongolic-Tungusic and Korean-Japanese-Ainu groupings were also posited by Joseph Greenberg (2000–2002); however, he treated them as independent members of a larger family, which he termed Eurasiatic. Anti-Altaicists Gerard Clauson (1956), Gerhard | "Altaic languages" | [
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3705 | Doerfer (1963), and Alexander Shcherbak argued 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. 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. Furthermore, they argued that many of the typological features | "Altaic languages" | [
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3706 | of the supposed Altaic languages, such as agglutinative morphology and subject–object–verb (SOV) word order, usually simultaneously occur in languages. In sum, the idea was that Turkic, Mongolic, and Tungusic languages form a "Sprachbund"—the result of convergence through intensive borrowing and long contact among speakers of languages that are not necessarily closely related. Doubt was also raised about the affinities of Korean and Japanese; in particular, some authors tried to connect Japanese to the Austronesian languages. Starostin's (1991) lexicostatistical research claimed that the proposed Altaic groups shared about 15–20% of potential cognates within a 110-word Swadesh-Yakhontov list (e.g. Turkic–Mongolic 20%, Turkic–Tungusic | "Altaic languages" | [
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3707 | 18%, Turkic–Korean 17%, Mongolic–Tungusic 22%, Mongolic–Korean 16%, Tungusic–Korean 21%). Altogether, Starostin concluded that the Altaic grouping was substantiated, though "older than most other language families in Eurasia, such as Indo-European or Finno-Ugric, and this is the reason why the modern Altaic languages preserve few common elements". Unger (1990) advocates a family consisting of Tungusic, Korean, and Japonic languages but not Turkic or Mongolic; and Doerfer (1988) rejects all the genetic claims over these major groups. In 2003, Claus Schönig published a critical overview of the history of the Altaic hypothesis up to that time. He concluded: In 2003, "An Etymological | "Altaic languages" | [
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3708 | Dictionary of the Altaic Languages" was published by Starostin, Dybo, and Mudrak. It contains 2,800 proposed cognate sets, a set of sound laws based on those proposed sets, and a number of grammatical correspondences, as well as a few important changes to the reconstruction of Proto-Altaic. For example, although most of today's Altaic languages have vowel harmony, Proto-Altaic as reconstructed by Starostin "et al." lacked it; instead, various vowel assimilations between the first and second syllables of words occurred in Turkic, Mongolic, Tungusic, Korean, and Japonic. It tries hard to distinguish loans between Turkic and Mongolic and between Mongolic and | "Altaic languages" | [
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3709 | Tungusic from cognates; and it suggests 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 (most of them already present in Starostin 1991), including words for such items as 'eye', 'ear', 'neck', 'bone', 'blood', 'water', 'stone', 'sun', and 'two'. This work has not changed the minds of any of the principal authors in the field, however. The debate continues unabated – e.g. S. Georg 2004, A. Vovin 2005, S. Georg 2005 (anti-Altaic); S. Starostin 2005, V. Blažek 2006, | "Altaic languages" | [
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3710 | M. Robbeets 2007, A. Dybo and G. Starostin 2008 (pro-Altaic). According to Roy Andrew Miller (1996: 98–99), the Clauson–Doerfer critique of Altaic relies exclusively on lexicon, whereas the fundamental evidence for Altaic comprises verbal morphology. Lars Johanson (2010: 15–17) suggests that a resolution of the Altaic dispute may yet come from the examination of verbal morphology and calls for a muting of the polemic: "The dark age of "pro" and "contra" slogans, unfair polemics, and humiliations is not yet completely over and done with, but there seems to be some hope for a more constructive discussion" (ib. 17). A 2015 | "Altaic languages" | [
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3711 | analysis using the Automated Similarity Judgment Program resulted in the Japonic languages being grouped with the Ainu and Austroasiatic languages, but showing no connection to Turkic and Mongolic. However, similarities between Ainu and Japonic are also due to extensive past contact. Analytic grammatical constructions acquired or transformed in Ainu were likely due to contact with Japanese and the Japonic languages, which had heavy influence on the Ainu languages with a large number of loanwords borrowed into the Ainu languages, and to a smaller extent, vice versa. The Ainu languages shows the least connection with Altaic. No genealogical relationship between Ainu | "Altaic languages" | [
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3712 | and any other language family has been demonstrated, despite numerous attempts. Thus, it is a language isolate. Ainu is sometimes grouped with the Paleosiberian languages, but this is only a geographic blanket term for several unrelated language families that were present in Siberia before the advances of Turkic and Tungusic languages there. The earliest known texts in a Turkic language are the Orkhon inscriptions, 720–735 AD. They were deciphered in 1893 by the Danish linguist Vilhelm Thomsen in a scholarly race with his rival, the German–Russian linguist Wilhelm Radloff. However, Radloff was the first to publish the inscriptions. The first | "Altaic languages" | [
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3713 | 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 inscription dated to 1224 or 1225 AD and by the "Secret History of the Mongols", written in 1228 (see Mongolic languages). The earliest Para-Mongolic text is the Memorial for Yelü Yanning, written in the Khitan Large Script and dated | "Altaic languages" | [
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3714 | to 986 AD. Japanese is first attested in a few short inscriptions from the 5th century AD, such as 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 that by the Man'yōshū, which dates from c. 771–785, 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 BC–668 AD), but are | "Altaic languages" | [
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3715 | preserved in an orthography that only goes back to the 9th century AD. Korean is copiously attested from the mid-15th century on in the phonetically precise Hangul system of writing. The prehistory of the peoples speaking these languages is largely unknown. Whereas for certain other language families, such as the speakers of Indo-European, Uralic, and Austronesian, we are able to frame substantial hypotheses, in the case of the proposed Altaic family much remains to be done. Some scholars bear in mind a possible Uralic and Altaic homeland in the Central Asian steppes. According to Juha Janhunen, the ancestral languages of | "Altaic languages" | [
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3716 | Turkic, Mongolic, Tungusic, Korean, and Japanese were spoken in a relatively small area comprising present-day North Korea, Southern Manchuria, and Southeastern Mongolia. However Janhunen (1992) is skeptical about an affiliation of Japanese to Altaic, while András Róna-Tas remarked that a relationship between Altaic and Japanese, if it ever existed, must be more remote than the relationship of any two of the Indo-European 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 languages" | [
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3717 | Altaic hypothesis formerly set the date of the Proto-Altaic language at around 4000 BC, but today at around 5000 BC or 6000 BC. This would make Altaic a language family about as old as Indo-European (4000 to 7,000 BC according to several hypotheses) but considerably younger than Afroasiatic (c. 10,000 BC or 11,000 to 16,000 BC according to different sources). "Note: This list is limited to linguists who have worked specifically on the Altaic problem since the publication of the first volume of Ramstedt's "Einführung" in 1952. The dates given are those of works concerning Altaic. For Altaicists, the version | "Altaic languages" | [
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3718 | of Altaic they favor is given at the end of the entry, if other than the prevailing one of Turkic–Mongolic–Tungusic–Korean–Japanese." Based on the proposed correspondences listed below, the following phoneme inventory has been reconstructed for the hypothetical Proto(-Macro)-Altaic language (taken from Blažek's [2006] summary of the newest Altaic etymological dictionary [Starostin et al. 2003] and transcribed into the ): This phoneme only occurred at the beginnings of words.<br> It is not clear whether , , were monophthongs as shown here (presumably ) or diphthongs (); the evidence is equivocal. In any case, however, they only occurred in the first (and | "Altaic languages" | [
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3719 | sometimes only) syllable of any word. Every vowel occurred in long and short versions which were different phonemes in the first syllable. Starostin et al. (2003) treat length together with pitch as a prosodic feature. As reconstructed by Starostin et al. (2003), Proto-Altaic was a pitch accent or tone language; at least the first and probably every syllable could have a high or a low pitch. If a Proto(-Macro)-Altaic language really existed, it should be possible to reconstruct regular sound correspondences between that protolanguage and its descendants; such correspondences would make it possible to distinguish cognates from loanwords (in many | "Altaic languages" | [
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3720 | cases). Such attempts have repeatedly been made. The latest version is reproduced here, taken from Blažek's (2006) summary of the newest Altaic etymological dictionary (Starostin et al. 2003) and transcribed into the . When a Proto-Altaic phoneme developed differently depending on its position in a word (beginning, interior, or end), the special case (or all cases) is marked with a hyphen; for example, Proto-Altaic disappears (marked "0") or becomes at the beginning of a Turkic word and becomes elsewhere in a Turkic word. Only single consonants are considered here. In the middle of words, clusters of two consonants were allowed | "Altaic languages" | [
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3721 | in Proto-Altaic as reconstructed by Starostin et al. (2003); the correspondence table of these clusters spans almost seven pages in their book (83–89), and most clusters are only found in one or a few of the reconstructed roots. Vowel harmony is pervasive in the languages attributed to Altaic: most Turkic and Mongolic as well as some Tungusic languages have it, Korean is arguably in the process of losing its traces, and it is controversially hypothesized for Old Japanese. (Vowel harmony is also typical of the neighboring Uralic languages and was often counted among the arguments for the Ural–Altaic hypotheses.) Nevertheless, | "Altaic languages" | [
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3722 | Starostin et al. (2003) reconstruct Proto-Altaic as lacking vowel harmony. Instead, according to them, vowel harmony originated in each daughter branch as assimilation of the vowel in the first syllable to the vowel in the second syllable (which was usually modified or lost later). "The situation therefore is very close, e.g. to Germanic [see Germanic umlaut] or to the Nakh languages in the Eastern Caucasus, where the quality of non-initial vowels can now only be recovered on the basis of umlaut processes in the first syllable." (Starostin et al. 2003:91) The table below is taken from Starostin et al. (2003): | "Altaic languages" | [
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3723 | Length and pitch in the first syllable evolved as follows according to Starostin et al. (2003), with the caveat that it is not clear which pitch was high and which was low in Proto-Altaic (Starostin et al. 2003:135). For simplicity of input and display every syllable is symbolized as "a" here: ¹ "Proto-Mongolian has lost all traces of the original prosody except for voicing *p > *b in syllables with original high pitch" (Starostin et al. 2003:135).<br> ² "[...] several secondary metatonic processes happened [...] in Korean, basically in the verb subsystem: all verbs have a strong tendency towards low | "Altaic languages" | [
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3724 | pitch on the first syllable." (Starostin et al. 2003:135) Starostin et al. (2003) have reconstructed the following correspondences between the case and number suffixes (or clitics) of the (Macro-)Altaic languages (taken from Blažek, 2006): /V/ symbolizes an uncertain vowel. Suffixes reconstructed for Proto-Turkic, Proto-Mongolic, Proto-Korean, or Proto-Japonic, but not attested in Old Turkic, Classical Mongolian, Middle Korean, or Old Japanese are marked with asterisks. This correspondences, however, have been harshly criticized for several reasons: There are significant gaps resulting in the absence of etymologies for certain initial segments: an impossible situation in the case of a genetic relationship; lack of | "Altaic languages" | [
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-0.5315930843353271,
-0.29482072591781616,
0.9622883200645447,
0.6656081676483154,
0.7513274550437927,
-0.042215652763843536,
-0.4768684506416321,
-0.04585646092891693,
0.1612781584262848,
-0.5028552412986755,
-0.2197607904672622... |
3725 | common paradigmatic morphology; in many cases, there are ghosts, invented or polished meanings; and word-list linguistics rules supreme, as there are few if any references to texts or philology. There are also many reconstructions proved to be totally false. For instance, regarding Korean, Starostin et al. state that Middle Korean genitive is /nʲ/, while it actually was /s/ in its honorific form, and /ój/ or /uj/ as neutral forms. In addition, some "cognates" are visibly forced, like the comparison between Turkish instrumental and Japanese locative /ni/. A locative postposition expresses an absolutely different meaning to that of an instrumental, so | "Altaic languages" | [
-0.5008083581924438,
0.1279718428850174,
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0.5209394693374634,
0.7254414558410645,
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0.1829981803894043,
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-0.3515270054340362... |
3726 | it is evident that both of them are not related whatsoever. The same applies for Japanese /ga/ and Proto Tungusic /ga/. The first of those particles expresses genitive case, while the second is the partitive case, which bear no resemblance of meaning at all either. Therefore, those two are not cognates. A different kind of issue is that of the Old Turkish genitive /Xŋ/ (where "X" stands for any phoneme) and Old Japanese genitive /no/. Although they share the same consonant, the fact that the former is a vowel plus a consonant, and the second is a fixed set of | "Altaic languages" | [
-0.31279146671295166,
0.248565211892128,
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-0.22791965305805206,
0.8253160715103149,
0.44287845492362976,
0.7911096811294556,
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0.02650471217930317,
0.11874373257160187,
-0.5283952951431274,
-0.2596265375614166... |
3727 | the consonant /n/ plus vowel /o/ makes the fact that those two are cognates extremely unlikely. The table below is taken (with slight modifications) from Blažek (2006) and transcribed into IPA. As above, forms not attested in Classical Mongolian or Middle Korean but reconstructed for their ancestors are marked with an asterisk, and /V/ represents an uncertain vowel. There are, however, several problems with this proposed list. Aside from the huge amount of non-attested, free reconstructions, some mistakes on the research carried out by altaicists must be pointed out. The first of them is that Old Japanese for the first | "Altaic languages" | [
-0.2943648397922516,
0.2975092828273773,
-0.5355123281478882,
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0.5277360677719116,
0.8948187232017517,
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0.020042041316628456,
0.07852867245674133,
-0.498747855424881,
-0.148192584514617... |
3728 | person pronoun ("I", in English) was neither /ba/ or /a/. It was /ware/ (和禮), and sometimes it was abbreviated to /wa/ (吾). Also, it is not a Sino-Japanese word, but a native Japanese term. In addition, the second person pronoun was not /si/, but either /imasi/ (汝), or /namu/ (奈牟), which sometimes was shortened to /na/. Its plural was /namu tachi/ (奈牟多知). The following table is a brief selection of further proposed cognates in basic vocabulary across the Altaic family (from Starostin et al. [2003]). Their reconstructions and equivalences are not accepted by the mainstream linguists and therefore remain very | "Altaic languages" | [
-0.42657700181007385,
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-0.6761899590492249,
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0.6495171189308167,
0.7324624061584473,
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-0.026105808094143867,
0.17096737027168274,
-0.6282647848129272,
-0.3313372135... |
3729 | controversial. In the Indo-European family, the numerals are remarkably stable. This is a rather exceptional case; especially words for higher numbers are often borrowed wholesale. (Perhaps the most famous cases are Japanese and Korean, which have two complete sets of numerals each – one native, one Chinese.) Indeed, the Altaic numerals are less stable than the Indo-European ones, but nevertheless Starostin et al. (2003) reconstruct them as follows. They are not accepted by the mainstream linguists and are controversial. Other reconstructions show little to no similarities in numerals of the proto-languages. Altaic languages Altaic () is a hypothesized language family | "Altaic languages" | [
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0.09655620157718658,
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-0.1883457154035... |
3730 | Austrian German Austrian German (), Austrian Standard German, 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 Germany, however, Standard Austrian German is still confused with some regional standard that is not considered "pure". This despite sound evidence that 80% of Austrian secondary school students and 90% of Austrian secondary school teachers consider German a pluricentric language, with more than one standard variety. In less formal situations, | "Austrian German" | [
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0.1528499722480774,
-0.38078680634498... |
3731 | Austrians tend to use forms closer to or identical with the Bavarian and Alemannic dialects, traditionally spoken – but rarely written – in Austria. Austrian German has its beginning in the mid-18th 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", 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 Popowitsch. | "Austrian German" | [
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-0.0623520128428936,
0.2430003434419632,
-0.1383780837059021,... |
3732 | Instead they decided for pragmatic reasons to adopt the already standardized Chancellery language of Saxony ("Sächsische Kanzleisprache" or "Meißner Kanzleideutsch"), which was based on the administrative language of the non-Austrian area of Meißen and Dresden. Thus Standard Austrian German has the same geographic origin as the Standard German of Germany ("Bundesdeutsches Hochdeutsch", also "Deutschländisches Deutsch") and 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 is defined | "Austrian German" | [
-0.10630477964878082,
0.535148024559021,
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-0.3053886890411377,
-0.07613396644592285,
0.17004390060901642,
-0.15092457830905914,... |
3733 | by the "Austrian Dictionary" (""), published under the authority of the Austrian Federal Ministry of Education, Arts and Culture. As German is a pluricentric language, Austrian German is merely one among several varieties of Standard German. Much like the relationship between British English and American English, the German varieties differ in minor respects (e.g., spelling, word usage and grammar) but are recognizably equivalent and largely mutually intelligible. The official Austrian dictionary, "das Österreichische Wörterbuch", prescribes grammatical and spelling rules defining the official language. Austrian delegates participated in the international working group that drafted the German spelling reform of 1996—several conferences | "Austrian German" | [
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0.22350649535655975,
0.09603695571422577,
-0.32696536183357... |
3734 | leading up to the reform were hosted in Vienna at the invitation of the Austrian federal government—and adopted it as a signatory, along with Germany, Switzerland, and Liechtenstein, of an international memorandum of understanding (Wiener Absichtserklärung) signed in Vienna in 1996. The "sharp s" (ß) is used in Austria, as in Germany. Because of the German language's pluricentric nature, German dialects in Austria should not be confused with the variety of Standard German spoken by most Austrians, which is distinct from that of Germany or Switzerland. Distinctions in vocabulary persist, for example, in culinary terms, where communication with Germans is | "Austrian German" | [
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0.07763691246509552,
0.031965408474206924,
-0.125637665390... |
3735 | frequently difficult, and administrative and legal language, which is due to Austria's exclusion from the development of a German nation-state in the late 19th century and its manifold particular traditions. A comprehensive collection of Austrian-German legal, administrative and economic terms is offered in "Markhardt, Heidemarie: Wörterbuch der österreichischen Rechts-, Wirtschafts- und Verwaltungsterminologie" (Peter Lang, 2006). The "former standard", used for about 300 years or more in speech in refined language, was the ', a sociolect spoken by the imperial Habsburg family and the nobility of Austria-Hungary. It differed from other dialects in vocabulary and pronunciation; it appears to have been | "Austrian German" | [
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0.48397818207740784,
0.4212329387664795,
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0.06401977688074112,
0.0451626218855381,
0.11784817278385162,... |
3736 | spoken with a slight degree of nasality. This was not a standard in a modern technical sense, as it was just the social standard of upper-class speech. 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 traditional form of the language, probably derived from medieval deeds and documents, and has a very complicated 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 | "Austrian German" | [
0.04184696450829506,
0.48511725664138794,
0.19478678703308105,
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0.1944696605205536,
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0.3894783854484558,
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-0.01699872873723507,
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-0.31751397252082... |
3737 | 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 German is replacing it in government and administrative texts. When Austria became a member of the European Union, the Austrian variety of the German language — limited to 23 agricultural terms — was "protected" in Protocol 10, regarding | "Austrian German" | [
0.017146209254860878,
0.501807451248169,
0.3383462131023407,
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0.4899134337902069,
0.538305401802063,
0.37072810530662537,
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0.004205496981... |
3738 | the use of Austrian-specific terms in the framework of the European Union, which forms part of the Austrian EU accession treaty. Austrian German is the only variety of a pluricentric language recognized under international law or EU primary law. All facts concerning “Protocol no. 10” are documented in Markhardt's "Das österreichische Deutsch im Rahmen der EU", Peter Lang, 2005. In Austria, as in the German-speaking 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 | "Austrian German" | [
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0.26061394810676575,
0.516201913356781,
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0.26048293709754944,
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0.1601615995168686,
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3739 | 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 (note: "ich bin geschlafen" is a rarely used form, more commonly "ich habe geschlafen" is used). 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""). | "Austrian German" | [
-0.22580452263355255,
0.4735206663608551,
0.51060950756073,
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0.7171186208724976,
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0.24223817884922028,
0.15518397092819214,
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... |
3740 | In addition, the preterite (simple past) is very rarely used in Austria, especially in the spoken language, with the exception of some modal verbs (i.e. "ich sollte", "ich wollte"). There are many official terms that differ in Austrian German from their usage in most parts of Germany. Words primarily used in Austria are "Jänner" (January) rather than "Januar", "Feber" (February) rather than "Februar", "heuer" (this year) rather than "dieses Jahr", "Stiege" (stairs) instead of "Treppe", "Rauchfang" (chimney) instead of "Schornstein", many administrative, legal and political terms – and a whole series of foods such as: "Erdäpfel" (potatoes) German "Kartoffeln" (but | "Austrian German" | [
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0.6833474636077881,
0.5579649209976196,
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0.3738333284854889,
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0.08468089252710342,
0.32617413997650146,
-0.178524225950241... |
3741 | Dutch "aardappel"), "Schlagobers" (whipped cream) German "Schlagsahne", "Faschiertes" (ground beef) German "Hackfleisch" (but Hungarian "fasírt", Croatian and Slovenian informal "faširano"), "Fisolen" (green beans) German "Gartenbohnen" (but Czech "fazole", Italian "fagioli", Croatian (regional) "fažol", Slovenian "fižol", Hungarian folkish "paszuly"), "Karfiol" (cauliflower) German "Blumenkohl" (but Croatian, Hungarian and Slovak "karfiol", Italian "cavolfiore"), "Kohlsprossen" (Brussels sprouts) German "Rosenkohl", "Marillen" (apricots) German "Aprikosen" (but Slovak "marhuľa", Polish "morela", Slovenian "marelice", Croatian "marelica"), "Paradeiser" ["Paradiesapfel"] (tomatoes) German "Tomaten" (but Hungarian "paradicsom", Slovak "paradajka", Slovenian "paradižnik", Serbian "paradajz"), "Palatschinken" (pancakes) German "Pfannkuchen" (but Czech "palačinky", Hungarian "palacsinta", Croatian and Slovenian "palačinke"), "Topfen" (a semi-sweet cottage cheese) | "Austrian German" | [
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0.25350335240364075,
0.27950093150138855,
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3742 | German "Quark" and "Kren" (horseradish) German "Meerrettich" (but Czech "křen", Slovak "chren", Croatian and Slovenian "hren", etc.). There are, however, some false friends between the two regional varieties: 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 Austro-Bavarian dialects are more intelligible to speakers of Standard German than the Southern Austro-Bavarian dialects of | "Austrian German" | [
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0.3061791658401489,
0.3019036650657654,
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... |
3743 | Tyrol. Viennese, the Austro-Bavarian 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 very 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 | "Austrian German" | [
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0.08037448674440384,
0.2528264820575714,
-0.1166992634534835... |
3744 | of the Tirol, 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 non-Germanic linguistic groups, such as the dialect of Carinthia, where in the past many speakers were bilingual with Slovene, and the | "Austrian German" | [
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0.09204432368278503,
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-0.21273423731327057,
0.15233179926872253,
0.08113894611597061,
-0.2087634354829788... |
3745 | dialect of Vienna, which has been influenced by immigration during the Austro-Hungarian period, particularly from what is today the Czech Republic. 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. Austrian German Austrian German (), Austrian Standard German, Standard Austrian German (), or Austrian High German (), is | "Austrian German" | [
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0.25437432527542114,
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0.002135385060682893,
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0.10689229518175125,
0.24694861471652985,
-0.22592337429523... |
3746 | Axiom of choice In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that "the Cartesian product of a collection of non-empty sets is non-empty". 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 formula_1 of nonempty sets there exists an indexed family formula_2 of elements such that formula_3 for every formula_4. The axiom | "Axiom of choice" | [
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3747 | of choice was formulated in 1904 by Ernst Zermelo in order to formalize his proof of the well-ordering 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. in <nowiki></nowiki> the smallest elements are {4, 10, 1}. In | "Axiom of choice" | [
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3748 | 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 non-empty subsets of the real numbers (if there are non-constructible reals). In that case, the axiom of choice must be invoked. Russell coined an analogy: for any (even infinite) collection of pairs of shoes, one can pick out the left | "Axiom of choice" | [
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3749 | 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, Zermelo–Fraenkel set theory with the axiom of choice (ZFC). One motivation for this use is that a number | "Axiom of choice" | [
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3750 | 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. A choice function is a function "f", defined on a collection "X" of nonempty sets, such that for every set "A" in "X", "f"("A") is an element of "A". With this concept, the axiom can | "Axiom of choice" | [
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3751 | 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. 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 | "Axiom of choice" | [
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3752 | 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: In this article and other discussions of the Axiom of Choice the following abbreviations are common: 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 | "Axiom of choice" | [
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3753 | by, in effect, replacing each choice function with its range. 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: Authors who use this formulation often speak of the "choice function on A", but be advised that this is a slightly different notion of choice function. Its domain is the powerset of "A" (with the empty set removed), and so makes sense for any set "A", whereas with the | "Axiom of choice" | [
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3754 | 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 which is equivalent to The negation of the axiom can thus be expressed as: 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 | "Axiom of choice" | [
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3755 | of the Zermelo–Fraenkel 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. Until the late 19th century, the axiom of choice was often used implicitly, although it had not yet been formally stated. For | "Axiom of choice" | [
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3756 | example, after having established that the set "X" contains only non-empty sets, a mathematician might have said "let "F(s)" be one of the members of "s" for all "s" in "X"." 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 have several (a finite number of) boxes, each containing at | "Axiom of choice" | [
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3757 | 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 | "Axiom of choice" | [
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3758 | 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 ("X" : "i"∈ω) 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 constructed, and no "limiting" choice function can be constructed, in general, in ZF without the axiom of choice. | "Axiom of choice" | [
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3759 | 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 | "Axiom of choice" | [
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3760 | 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 non-empty 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 procedure 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. | "Axiom of choice" | [
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3761 | 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 "x"/2, and "x"/2 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 "π". Here "G" is countable while "S" is uncountable. Hence "S" breaks up into uncountably many orbits under "G". Using the | "Axiom of choice" | [
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3762 | 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 congruent. Since "X" is not measurable for any rotation-invariant countably additive finite measure on "S", finding an algorithm to select a point in each orbit requires the axiom of choice. See non-measurable set for more details. The reason that we are able to choose least elements from subsets | "Axiom of choice" | [
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3763 | of the natural numbers is the fact that the natural numbers are well-ordered: 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 well-ordering. Then our choice function can choose the least element of every set under our unusual ordering." The problem then becomes that of constructing a well-ordering, which turns out to require the axiom of choice for its existence; every set | "Axiom of choice" | [
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3764 | can be well-ordered if and only if the axiom of choice holds. A proof requiring the axiom of choice may establish the existence 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 well-ordering of the real numbers, there are models of set theory with the axiom of choice in which no well-ordering 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 | "Axiom of choice" | [
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3765 | 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 well-ordering of all sets, a construction that relies on a well-ordering 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 | "Axiom of choice" | [
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3766 | of objects that may seem counterintuitive. One example is the Banach–Tarski paradox which says that it is possible to decompose the 3-dimensional 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 non-measurable 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 | "Axiom of choice" | [
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3767 | 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 negation; 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 | "Axiom of choice" | [
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3768 | claim that relies on either the axiom of choice or its negation unprovable. For example, the Banach–Tarski 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 Banach–Tarski paradox | "Axiom of choice" | [
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3769 | can be rephrased as conditional statements, for example, "If AC holds, then the decomposition in the Banach–Tarski paradox exists." Such conditional statements are provable in ZF when the original statements are provable from ZF and the axiom of choice. 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 non-classical logic is employed. The status of | "Axiom of choice" | [
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3770 | the axiom of choice varies between different varieties of constructive mathematics. In Martin-Löf type theory and higher-order 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 Martin-Löf 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 | "Axiom of choice" | [
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3771 | 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. In 1938, Kurt Gödel showed that the "negation" of the axiom of choice is not a theorem of ZF by constructing an inner model (the | "Axiom of choice" | [
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3772 | 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 by constructing a much more complex model which satisfies ZF¬C (ZF with the negation of AC added as axiom) and thus showing that ZF¬C 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 | "Axiom of choice" | [
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3773 | 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 | "Axiom of choice" | [
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3774 | 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 independence 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 | "Axiom of choice" | [
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3775 | 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. The axiom | "Axiom of choice" | [
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3776 | 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 Neumann–Bernays–Gödel set theory and Morse–Kelley 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. 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 | "Axiom of choice" | [
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3777 | are Zorn's lemma and the well-ordering theorem. In fact, Zermelo initially introduced the axiom of choice in order to formalize his proof of the well-ordering theorem. 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 hom-objects are sets, then there is | "Axiom of choice" | [
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3778 | no category of all sets, and so it is difficult for a category-theoretic formulation to apply to all sets. On the other hand, other foundational descriptions of category theory are considerably stronger, and an identical category-theoretic statement of choice may be stronger than the standard formulation, à la class theory, mentioned above. Examples of category-theoretic statements which require choice include: 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), | "Axiom of choice" | [
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3779 | 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 Lebesgue 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 the existence of an ultrafilter containing each given filter, proved by Tarski in 1930. One of the most interesting aspects of the axiom of | "Axiom of choice" | [
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3780 | 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. There are several historically important set-theoretic statements implied by AC whose equivalence to AC is open. The partition principle, which was formulated before AC itself, was cited by Zermelo as a justification for believing AC. In 1906 Russell declared PP to be | "Axiom of choice" | [
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3781 | 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. Now, consider stronger forms of the negation of AC. For example, 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 | "Axiom of choice" | [
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3782 | single set of nonempty sets. Note that 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 that every set of reals is Lebesgue measurable, has the property of Baire, and has the perfect set | "Axiom of choice" | [
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3783 | 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. There are models of Zermelo-Fraenkel set theory in which the axiom of choice is false. We shall abbreviate "Zermelo-Fraenkel set theory plus the negation of the | "Axiom of choice" | [
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3784 | axiom of choice" by ZF¬C. For certain models of ZF¬C, it is possible to prove the negation of some standard facts. Note that any model of ZF¬C 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. For each of the following statements, there is some model of ZF¬C where it is true: For proofs, see . In type theory, a different kind of statement is known as the axiom of choice. This form begins with two types, σ and τ, and a relation "R" | "Axiom of choice" | [
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3785 | between objects of type σ and objects of type τ. The axiom of choice states that if for each "x" of type σ there exists a "y" of type τ such that "R"("x","y"), then there is a function "f" from objects of type σ to objects of type τ such that "R"("x","f"("x")) holds for all "x" of type σ: 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. This is a joke: although the three | "Axiom of choice" | [
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3786 | are all mathematically equivalent, many mathematicians find the axiom of choice to be intuitive, the well-ordering 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. Polish-American mathematician Jan Mycielski relates this anecdote in a 2006 article in the Notices of the | "Axiom of choice" | [
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3787 | AMS. This quote comes from the famous April Fools' Day article in the "computer recreations" column of the "Scientific American", April 1989. Axiom of choice In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that "the Cartesian product of a collection of non-empty sets is non-empty". 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 | "Axiom of choice" | [
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3788 | Attila Attila (; fl. c. 406–453), 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, and Alans among others, in Central and Eastern Europe. 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 | Attila | [
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3789 | 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 (Orléans) before being defeated at 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 died 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. There is no surviving first-hand account of Attila's appearance, but there | Attila | [
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3790 | is a possible second-hand 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. Many scholars have argued that 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". The Gothic | Attila | [
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3791 | etymology was first proposed by Jacob and Wilhelm Grimm in the early 19th century. Maenchen-Helfen notes that this derivation of the name "offers neither phonetic nor semantic difficulties", and Gerhard Doerfer notes that the name is simply correct Gothic. 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 "Ἀττίλα" (Attíla) a composite title-name which derived from Turkic *"es" (great, old), and *"t il" (sea, ocean), and the suffix /a/. The stressed back syllabic "til" assimilated the front member "es", so | Attila | [
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3792 | it became *"as". It is a nominative, in form of "attíl-" (< *"etsíl" < *"es tíl") with the meaning "the oceanic, universal ruler". J.J. Mikkola connected it with Turkic "āt" (name, fame). As another Turkic possibility, H. Althof (1902) considered it was related to Turkish "atli" (horseman, cavalier), or Turkish "at" (horse) and "dil" (tongue). Maenchen-Helfen argues that these derivations are "ingenious but for many reasons unacceptable". M. Snædal 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 England had | Attila | [
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3793 | a name of Greek origin, and Süleyman 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. Snædal, 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 Turkic-Mongolian "at, adyy/agta" (gelding, warhorse) and Turkish "atli" (horseman, cavalier), meaning "possessor of geldings, provider of warhorses". The historiography of | Attila | [
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3794 | Attila is faced with a major challenge, in that the only complete sources are written in Greek and Latin by the enemies of the Huns. Attila's contemporaries left many testimonials of his life, but only fragments of these remain. Priscus was a Byzantine diplomat and historian who wrote in Greek, and he was both a witness to and an actor in the story of Attila, as a member of the embassy of Theodosius II at the Hunnic court in 449. He was obviously biased by his political position, but his writing is a major source for information on the life | Attila | [
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3795 | of Attila, and he is the only person known to have recorded a physical description of him. He wrote a history of the late Roman Empire in eight books covering the period from 430 to 476. Today we have only fragments of Priscus' work, but it was cited extensively by 6th-century historians Procopius and Jordanes, especially in Jordanes' "The Origin and Deeds of the Goths". It contains numerous references to Priscus's history, and it is also an important source of information about the Hunnic empire and its neighbors. He describes the legacy of Attila and the Hunnic people for a | Attila | [
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3796 | century after Attila's death. Marcellinus Comes, a chancellor of Justinian during the same era, also describes the relations between the Huns and the Eastern Roman Empire. Numerous ecclesiastical writings contain useful but scattered information, sometimes difficult to authenticate or distorted by years of hand-copying between the 6th and 17th centuries. The Hungarian writers of the 12th century wished to portray the Huns in a positive light as their glorious ancestors, and so repressed certain historical elements and added their own legends. The literature and knowledge of the Huns themselves was transmitted orally, by means of epics and chanted poems that | Attila | [
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3797 | were handed down from generation to generation. Indirectly, fragments of this oral history have reached us via the literature of the Scandinavians and Germans, neighbors of the Huns who wrote between the 9th and 13th centuries. Attila is a major character in many Medieval epics, such as the Nibelungenlied, as well as various Eddas and sagas. Archaeological investigation has uncovered some details about the lifestyle, art, and warfare of the Huns. There are a few traces of battles and sieges, but today the tomb of Attila and the location of his capital have not yet been found. The Huns were | Attila | [
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3798 | a group of Eurasian nomads, appearing from east of the Volga, who migrated further into Western Europe c. 370 and built up an enormous empire there. Their main military techniques were mounted archery and javelin throwing. They were in the process of developing settlements before their arrival in Western Europe, yet the Huns were a society of pastoral warriors whose primary form of nourishment was meat and milk, products of their herds. The origin and language of the Huns has been the subject of debate for centuries. According to some theories, their leaders at least may have spoken a Turkic | Attila | [
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3799 | language, perhaps closest to the modern Chuvash language. One scholar suggests a relationship to Yeniseian. According to the "Encyclopedia of European Peoples", "the Huns, especially those who migrated to the west, may have been a combination of central Asian Turkic, Mongolic, and Ugric stocks". Attila's father Mundzuk was the brother of kings Octar and Ruga, who reigned jointly over the Hunnic empire in the early fifth century. This form of diarchy was recurrent with the Huns, but historians are unsure whether it was institutionalized, merely customary, or an occasional occurrence. His family was from a noble lineage, but it is | Attila | [
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3800 | uncertain whether they constituted a royal dynasty. Attila's birthdate is debated; journalist Éric Deschodt and writer Herman Schreiber have proposed a date of 395. However, historian Iaroslav Lebedynsky and archaeologist Katalin Escher prefer an estimate between the 390s and the first decade of the fifth century. Several historians have proposed 406 as the date. Attila grew up in a rapidly changing world. His people were nomads who had only recently arrived in Europe. They crossed the Volga river during the 370s and annexed the territory of the Alans, then attacked the Gothic kingdom between the Carpathian mountains and the Danube. | Attila | [
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