An appreciation of Kreisel. (English) Zbl 0895.01006

Nerode, Anil

Odifreddi, Piergiorgio (ed.), Kreiseliana: about and around Georg Kreisel. Wellesley, MA: A K Peters. 81-88 (1996).

The author reports on his relations to Georg Kreisel, starting with reading experiences when being a graduate mathematics student at Chicago, with some reflections on Kreisel’s style of writing and the import of his papers. He reports on his first meeting with Kreisel at the 1957 AMS Summer Institute in Symbolic Logic, organized by J. Barkley Rosser at Cornell.
Reflections on his own research on models of intuitionistic Zermelo-Fraenkel set theory lead the author to some insights on the unity of mathematics in its polymorphism: “Very often I think that what we all think is individual creativity is mostly determined by the historical epoch in which we work. Thus, subjects that looked quite different thirty years ago seem much the same thirty years later” (p. 85).
The author regards the following two of Kreisel’s contributions to logic as his mathematical heritage: the Kreisel-Troelstra realizability interpretation for higher-order intuitionistic logic and Kreisel’s recursion theory on the ordinals.
For the entire collection see [Zbl 0894.03002].

Reviewer: V.Peckhaus (Erlangen)

MSC:

01A70	Biographies, obituaries, personalia, bibliographies
03-03	History of mathematical logic and foundations

Keywords:

reminiscences; modells of intuitionistic Zermelo-Fraenkel set theory; isols; higher order intuitionistic type theory; recursion theory on the ordinals