Jacques Herbrand

Jacques Herbrand ( born February 12, 1908 in Paris, † July 27, 1931 in La Bérarde ) was a French logician, algebraists and number theorists.

Life

Herbrand was in the national entrance examinations for the École Normale Supérieure (ENS ) in 1925 first and was the best student of ENS in the final exams 1928. Already at that time he became interested in mathematical logic to interest (which was generally not studied in France ) and read the Principia Mathematica by Bertrand Russell and Alfred North Whitehead. In 1929, he was with Ernest Vessiot his doctorate with a thesis in mathematical logic.

After his military service, he went with a Rockefeller Fellowship in 1931 to John von Neumann at the Humboldt University of Berlin, Emil Artin at the University of Hamburg and Emmy Noether at Göttingen University. Prior to his return to France he wanted to spend a vacation in the Alps and had an accident there deadly age of 23 while mountain climbing. Emmy Noether regretted in an obituary: One of the strongest mathematical talents is passed away with him from the midst of intense work out, full of ideas for the future.

Within the framework of Hilbert's program of finitistic foundation of mathematics Herbrand was a proof of the consistency of a specific area of arithmetic with restricted induction. He began already in his thesis in Paris and put it later during his stay in Germany in 1930 continued. Evidence of consistency of parts of the arithmetic tasks that Wilhelm Ackermann ( 1924) and John von Neumann ( 1927). After the incompleteness theorem of Kurt Gödel (1930 ), a consistency proof of full arithmetic is not possible, which Herbrand then learned about John von Neumann and what he still considered in his essay of 1931, which was received at his death in Crelle Journal. He also corresponded with Kurt Gödel on the concept of recursive functions.

According to him, among other things, the Herbrand universe and the set of Herbrand named in the predicate logic. His findings are summarized in the predicate logic as Herbrand theory.

Herbrand also made ​​significant contributions to algebraic number theory, although he was only a few months involved therein (a total of ten published works by him to do so). His studies -boyfriend Claude Chevalley published some of his work after his death.

His awards honor the Academie des Sciences, the Prix Jacques Herbrand.

Writings

  • Sur la théorie de la démonstration, Comptes rendus Acad. Sci., Paris, Volume 186, 1928, pp. 1274-1276
  • Non- contradiction of the axiom arithméthiques, Comptes rendus Acad. Sci., Paris, Volume 188, 1929, pp. 303-304
  • Sur quelques propriétés of propositions vraies et leurs applications, Comptes rendus Acad. Sci., Volume 188, 1929, pp. 1076-1078
  • Sur le problème fundamental of Mathématiques, Comptes rendus Acad. Sci., Volume 189, 1929, pp. 554-556, 720
  • Sur le problème de la logique fundamental mathématique, Comptes Rendus Soc. Sci. et L. de Varsovie, 1931
  • Les bases de la logique hilbertienne, Revue de métaphysique et de morale, Volume 37, 1930, pp. 243-255
  • Recherches sur la théorie de la démonstration, Thesis, University of Paris 1930 (. . Travaux and Soc Sci et de Varsovie L. ) Online, English translation: Investigations in proof theory: the properties of true dispositions, 1930, in Jean Van Heijenoort (Editor ) From Frege to Gödel, Harvard University Press 1967, p 525
  • On the theory of algebraic functions ( from letters to Emmy Noether ), Mathematische Annalen, Vol 106, 1932, S. 52 ( posthumous releases of results of Herbrand by Emmy Noether )
  • Théorie des corps de nombres de arithmétique degré infini, Part I: Extensions algébriques Finies de corps infinie, Mathematische Annalen, Vol 106, 1932, p 473 ( with obituary of Emmy Noether ), Part II: Extensions algébriques de degré infini, Mathematische Annalen, Volume 109, 1933, p 699 ( from the estate of Claude Chevalley )
  • Sur la non- contradiction de l' arithmétique, Journal of Pure and Applied Mathematics, Volume 166, 1931, pp. 1-8 ( with foreword by Helmut Hasse ), English translation in Heijenoort From Frege to Gödel, Harvard UP, 1967, The consistency of arithmetic, pp. 618-628
Term algebra Herbrand's theorem Herbrand structure Herbrand-Award Integrated Authority File
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