Géza Fodor (mathematician)
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Géza Fodor (mathematician)
Géza Fodor (6 May 1927 in Szeged – 28 September 1977 in Szeged) was a Hungarian mathematician, working in set theory. He proved Fodor's lemma on stationary sets, one of the most important, and most used results in set theory. He was a professor at the Bolyai Institute of Mathematics at the Szeged University. He was vice-president, then president of the Szeged University. He was elected a corresponding member of the Hungarian Academy of Sciences The Hungarian Academy of Sciences ( hu, Magyar Tudományos Akadémia, MTA) is the most important and prestigious learned society of Hungary. Its seat is at the bank of the Danube in Budapest, between Széchenyi rakpart and Akadémia utca. Its ma .... 1927 births 1977 deaths Members of the Hungarian Academy of Sciences Set theorists 20th-century Hungarian mathematicians People from Szeged {{Europe-mathematician-stub ...
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Géza Fodor (1927-1977) Hungarian Mathematician
Géza Fodor may refer to: *Géza Fodor (mathematician) Géza Fodor (6 May 1927 in Szeged – 28 September 1977 in Szeged) was a Hungarian mathematician, working in set theory. He proved Fodor's lemma on stationary sets, one of the most important, and most used results in set theory. He was a pr ... (1927–1977), Hungarian mathematician * Géza Fodor (philosopher) (1943–2008), Hungarian art and literary critic {{Hndis, Fodor, Geza ...
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Szeged
Szeged ( , ; see also #Etymology, other alternative names) is List of cities and towns of Hungary#Largest cities in Hungary, the third largest city of Hungary, the largest city and regional centre of the Southern Great Plain and the county seat of Csongrád-Csanád County, Csongrád-Csanád county. The University of Szeged is one of the most distinguished universities in Hungary. The Szeged Open Air (Theatre) Festival (first held in 1931) is one of the main attractions, held every summer and celebrated as the Day of the City on 21 May. Etymology The name ''Szeged'' might come from an old Hungarian language, Hungarian word for 'corner' (), pointing to the turn of the river Tisza that flows through the city. Others say it derives from the Hungarian word which means 'island'. Others still contend that means 'dark blond' () – a reference to the color of the water where the rivers Tisza and Mureș (river), Maros merge. The city has its own name in a number of foreign language ...
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Hungarian People
Hungarians, also known as Magyars ( ; hu, magyarok ), are a nation and ethnic group native to Hungary () and Kingdom of Hungary, historical Hungarian lands who share a common Hungarian culture, culture, Hungarian history, history, Magyar tribes, ancestry, and Hungarian language, language. The Hungarian language belongs to the Uralic languages, Uralic language family. There are an estimated 15 million ethnic Hungarians and their descendants worldwide, of whom 9.6 million live in today's Hungary. About 2–3 million Hungarians live in areas that were part of the Kingdom of Hungary before the Treaty of Trianon in 1920 and are now parts of Hungary's seven neighbouring countries, Hungarians in Slovakia, Slovakia, Hungarians in Ukraine, Ukraine, Hungarians in Romania, Romania, Hungarians in Serbia, Serbia, Hungarians of Croatia, Croatia, Prekmurje, Slovenia, and Hungarians in Austria, Austria. Hungarian diaspora, Significant groups of people with Hungarian ancestry live in various oth ...
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Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ...
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Set Theory
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was initiated by the German mathematicians Richard Dedekind and Georg Cantor in the 1870s. In particular, Georg Cantor is commonly considered the founder of set theory. The non-formalized systems investigated during this early stage go under the name of '' naive set theory''. After the discovery of paradoxes within naive set theory (such as Russell's paradox, Cantor's paradox and the Burali-Forti paradox) various axiomatic systems were proposed in the early twentieth century, of which Zermelo–Fraenkel set theory (with or without the axiom of choice) is still the best-known and most studied. Set theory is commonly employed as a foundational ...
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Fodor's Lemma
In mathematics, particularly in set theory, Fodor's lemma states the following: If \kappa is a regular, uncountable cardinal, S is a stationary subset of \kappa, and f:S\rightarrow\kappa is regressive (that is, f(\alpha)<\alpha for any \alpha\in S, \alpha\neq 0) then there is some \gamma and some stationary S_0\subseteq S such that f(\alpha)=\gamma for any \alpha\in S_0. In modern parlance, the nonstationary ideal is ''normal''. The lemma was first proved by the Hungarian set theorist, Géza Fodor in 1956. It is sometimes also called "The Pressing Down Lemma".


Proof

We can assume that 0\notin S (by removing 0, if necessary). If Fodor's lemma is false, for every \alpha<\kappa there is some

Stationary Set
In mathematics, specifically set theory and model theory, a stationary set is a set that is not too small in the sense that it intersects all club sets, and is analogous to a set of non-zero measure in measure theory. There are at least three closely related notions of stationary set, depending on whether one is looking at subsets of an ordinal, or subsets of something of given cardinality, or a powerset. Classical notion If \kappa is a cardinal of uncountable cofinality, S \subseteq \kappa, and S intersects every club set in \kappa, then S is called a stationary set.Jech (2003) p.91 If a set is not stationary, then it is called a thin set. This notion should not be confused with the notion of a thin set in number theory. If S is a stationary set and C is a club set, then their intersection S \cap C is also stationary. This is because if D is any club set, then C \cap D is a club set, thus (S \cap C) \cap D = S \cap (C \cap D) is non empty. Therefore, (S \cap C) must be stati ...
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Szeged University
, mottoeng = Truth. Bravery. Freedom. , established = , type = Public research university , founder = Emperor Franz Joseph I , affiliation = European University Association, Science Without Borders, Confucius Institute , budget = US$220 million , chancellor = Judit Fendler , rector = László Rovó , students = 22,693 , undergrad = 17,384 , postgrad = 2,668 , doctoral = 714 , other = 3,997 (international) , city = Szeged , country = Hungary , coordinates = , campus = Urban , language = Hungarian, English , colours = Blue , website = , academic_staff = 1,968 , administrative_staff = 2,200 The University of Szeged ( hu, Szegedi Tudományegyetem, ) is a public research university in Szeged, Hungary. Established as the Jesuit Academy of Kolozsvár in present-day Cluj-Napoca in 1581, the institution was re-established as a university in 1872 by Emperor Franz Joseph I. The university relocated to Szeged in 1921, making it one of the oldest research universitie ...
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University Of Szeged
, mottoeng = Truth. Bravery. Freedom. , established = , type = Public research university , founder = Emperor Franz Joseph I , affiliation = European University Association, Science Without Borders, Confucius Institute , budget = US$220 million , chancellor = Judit Fendler , rector = László Rovó , students = 22,693 , undergrad = 17,384 , postgrad = 2,668 , doctoral = 714 , other = 3,997 (international) , city = Szeged , country = Hungary , coordinates = , campus = Urban , language = Hungarian, English , colours = Blue , website = , academic_staff = 1,968 , administrative_staff = 2,200 The University of Szeged ( hu, Szegedi Tudományegyetem, ) is a public research university in Szeged, Hungary. Established as the Jesuit Academy of Kolozsvár in present-day Cluj-Napoca in 1581, the institution was re-established as a university in 1872 by Emperor Franz Joseph I. The university relocated to Szeged in 1921, making it one of the oldest research universitie ...
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Hungarian Academy Of Sciences
The Hungarian Academy of Sciences ( hu, Magyar Tudományos Akadémia, MTA) is the most important and prestigious learned society of Hungary. Its seat is at the bank of the Danube in Budapest, between Széchenyi rakpart and Akadémia utca. Its main responsibilities are the cultivation of science, dissemination of scientific findings, supporting research and development, and representing Hungarian science domestically and around the world. History The history of the academy began in 1825 when Count István Széchenyi offered one year's income of his estate for the purposes of a ''Learned Society'' at a district session of the Diet in Pressburg (Pozsony, present Bratislava, seat of the Hungarian Parliament at the time), and his example was followed by other delegates. Its task was specified as the development of the Hungarian language and the study and propagation of the sciences and the arts in Hungarian. It received its current name in 1845. Its central building was inaugurate ...
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1927 Births
Nineteen or 19 may refer to: * 19 (number), the natural number following 18 and preceding 20 * one of the years 19 BC, AD 19, 1919, 2019 Films * ''19'' (film), a 2001 Japanese film * ''Nineteen'' (film), a 1987 science fiction film Music * 19 (band), a Japanese pop music duo Albums * ''19'' (Adele album), 2008 * ''19'', a 2003 album by Alsou * ''19'', a 2006 album by Evan Yo * ''19'', a 2018 album by MHD * ''19'', one half of the double album ''63/19'' by Kool A.D. * ''Number Nineteen'', a 1971 album by American jazz pianist Mal Waldron * ''XIX'' (EP), a 2019 EP by 1the9 Songs * "19" (song), a 1985 song by British musician Paul Hardcastle. * "Nineteen", a song by Bad4Good from the 1992 album '' Refugee'' * "Nineteen", a song by Karma to Burn from the 2001 album ''Almost Heathen''. * "Nineteen" (song), a 2007 song by American singer Billy Ray Cyrus. * "Nineteen", a song by Tegan and Sara from the 2007 album '' The Con''. * "XIX" (song), a 2014 song by Slipk ...
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