László Kalmár

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László

László Kalmár (Hungarian: Kalmár László [ˈkɒlmaːr ˈlaːsloː]; 27 March 1905, Edde – 2 August 1976, Mátraháza) was a Hungarian mathematician and Professor at the University of Szeged. Kalmár is considered the founder of mathematical logic and theoretical computer science in Hungary.

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Biography Kalmár was of Jewish ancestry. His early life mixed promise and tragedy. His father died when he was young, and his mother died when he was 17, the year he entered the University of Budapest, making him essentially an orphan. Kalmár's brilliance manifested itself while in Budapest schools. At the University of Budapest, his teachers included Kürschák and Fejér. His fellow students included the future logician Rózsa Politzer, from 1934 on Rózsa Péter. Kalmár graduated in 1927. He discovered mathematical logic, his chosen field, while visiting Göttingen in 1929. Upon completing his doctorate at Budapest, he took up a position at the University of Szeged. That university was mostly made up of staff from the former University of Kolozsvár, a major Hungarian university before World War I that found itself after the War in Romania. Kolozsvár was renamed Cluj. The Hungarian university moved to Szeged in 1920, where there had previously been no university. The appointment of Haar and Riesz turned Szeged into a major research center for mathematics. Kalmár began his career as a research assistant to Haar and Riesz. Kalmár was appointed a full professor at Szeged in 1947. He was the inaugural holder of Szeged's chair…Citește mai mult

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Elementary functions Kalmár defined what are known as elementary recursive functions (i.e. those based on the natural numbers) built up from the notions of composition and variables, the constants 0 {\displaystyle 0} and 1 {\displaystyle 1} , repeated addition + {\displaystyle +} of the constants, proper subtraction − ˙ {\displaystyle \mathbin {\dot {-}} } , bounded summation and bounded product. Elimination of the bounded product from this list yields the subelementary or lower elementary functions. By use of the abstract computational model called a register machine, Schwichtenberg provides a demonstration that "all elementary functions are computable and totally defined".

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References Hersh, Reuben; John-Steiner, Vera (June 1993). "A visit to Hungarian mathematics". Mathematical Intelligencer. 15 (2): 13–26. doi:10.1007/BF03024187. S2CID 122827181. Retrieved 8 November 2023. Kalmár, László (1937). "Zurückführung des Entscheidungsproblems auf den Fall von Formeln mit einer einzigen binären Funktionsvariablen\". Compositio Mathematica (in German). 4: 137–144. Kalmár, László (1943). "Egyszerű példa eldönthetetlen aritmetikai problémára" [Ein einfaches Beispiel für ein unentscheidbares arithmetisches Problem]. Matematikai és Fizikai Lapok (in Hungarian). 50. Budapest: 1–23. Hungarian with German abstract. Kalmár, László (1959). "An Argument Against the Plausibility of Church's Thesis". In Heyting, Arend (ed.). Constructivity in Mathematics. Amsterdam: North-Holland. Kleene, Stephen Cole (1952). Introduction to Metamathematics. New York: Van Nostrand. OCLC 523942.reprint. Ishi Press. 13 March 2009 [1952]. ISBN 9780923891572. Schwichtenberg, Helmut. "Computability". see under "Computability" Schwichtenberg, Helmut (2007). "Recursion Theory (Notes for a lecture course)". Retrieved 8 November 2023. Szabó, Máté (January 2018). "Kalmár's Argument Against the Plausibility of Church's Thesis". History and Philosophy of Logic. 39 (2): 140–157. doi:10.1080/01445340.2017.1396520. S2CID 126267583.

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László Kalmár at the Mathematics Genealogy Project "MacTutor". 2000. Retrieved 8 November 2023. The source for most of this entry