Jean-Louis Krivine

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Jean-Louis Krivine (* 1939 ) is a French mathematical logician and mathematician.

Life

He studied from 1957 at the École normal supérieure (ENS) with a degree in mathematics in 1960. In 1967 he received his doctorate under Jean-Pierre Kahane (Doctorat d'Etat). He was a professor at the University of Paris VII (Denis Diderot) and a member of the Laboratory for Evidence, Programs and Systems ( Preuves, Programs et Systèmes ). He has now retired, but is still active in mathematics (2011).

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In set theory and logic, in the 1980s he turned the interface between logic and computer science to the context of the connection between proofs of mathematical logic and programs described by the Curry-Howard correspondence , the full scope of which was then recognized and taken up by a new generation of researchers . Krivine developed a program around this concept of feasibility and applied it in the 2000s to axiomatic set theory in order to gain new models of Zermelo Fraenkel set theory that are not based on the forcing concept.

He also dealt with Banach spaces , where he made significant contributions in the 1960s and 1970s. With Dacunha-Castelle he introduced ultra-products into the theory of Banach spaces and in 1977 he found the best upper bound for the Grothendieck constant in the real case. With Bernard Maurey he introduced the concept of stable Banach spaces. Krivine's theorem about the finite representability of in a Banach space is named after him.

He also made contributions to real algebraic geometry in 1964, which anticipated later developments, but were not taken into account in the development of the theory that began in the early 1970s and were found independently by other mathematicians (for example, the theorem of Kadison and Dubois).

He wrote several textbooks, including on the lambda calculus (an abstract machine for reducing lambda terms is known as the Krivine machine), model theory and axiomatic set theory , some of which have also been translated into English and German.

In 2004 he received the Prix du Rayonnement Francais.

His doctoral students include Jean-Yves Girard , Daniel Lascar , Jacques Stern , Serge Grigorieff .

Fonts

  • Lambda calculus - types and models , Ellis Horwood, New York 1993 (French original from Masson 1990)
  • Théorie axiomatique des ensembles , Presses universitaires de France, Paris 1972 (English translation: Introduction to axiomatic set theory , Dordrecht, Reidel 1971)
  • Théore des ensembles , Cassini, Paris, 1998, 2nd edition 2007
  • with Georg Kreisel : Elements of mathematical logic (model theory) , North Holland 1967 (French original Dunod 1966)
    • German translation: Model theory: an introduction to mathematical logic and basic theory , Springer Verlag 1972

Web links

Individual evidence

  1. ↑ Date of birth according to Albrecht Pietsch History of Banach Spaces and Linear Operators , 2007
  2. ^ Title of the dissertation Sous-espaces et cones convexes dans les espaces , Mathematics Genealogy Project
  3. ↑ Krivine Constantes de Grothendieck et fonctions de type positif sur les spheres , Advances in Mathematics, Volume 31, 1979, pp. 16-30
  4. ^ Krivine, Maurey Espaces des Banach stable , Israel J. Math., Vol. 39, 1981, pp. 273-295
  5. ↑ Krivine Sous-espaces de dimension finie des espaces Banach réticulés , Annals of Mathematics, Volume 116, 1976, pp. 1-29
  6. ↑ Anneaux préordonneés , Journal d´Analyse Mathematique, Volume 12, 1964, pp. 307–326
  7. ^ Curien, Pisier, Gazette des Mathematiciens, Volume 104, 2005, p. 99. A. Prestel, N. Delzell Positive Polynomials , Springer 2001
  8. ^ Gazette des Mathematiciens, April 2005, p. 99, appreciation of Pierre-Louis Curien and Gilles Pisier
personal data
SURNAME Krivine, Jean-Louis
BRIEF DESCRIPTION French mathematical logician and mathematician
DATE OF BIRTH 1939