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Mathematical intuitionism. Introduction to proof theory. Transl. from the Russian by E. Mendelson, ed. by Ben Silver. (English) Zbl 0634.03054

Translations of Mathematical Monographs, 67. Providence, RI: American Mathematical Society (AMS). IX, 228 p.; $ 75.00 (1988).
[For a review of the Russian original (Moskva, 1979) see Zbl 0439.03041.]
This monograph is intended to present the most important methods of proof theory in intuitionistic logic, assuming the reader to have mastered an introductory course in mathematical logic. The book consists of five parts and two appendices. The first part is devoted to purely syntactical methods based on Gentzen’s cut-elimination theorem. The second part deals with intuitionistic arithmetic, where Kleene’s realizability method plays a central role. The third part is concerned with algebraic models and completeness theorems for them. The fourth part, which is a survey in nature, deals with the principles of intuitionistic analysis. The fifth part is concerned with the cut-elimination theorem in intuitionistic simple theory of types with an extensionality rule.
Reviewer: H.Nishimura

MSC:

03Fxx Proof theory and constructive mathematics
03F55 Intuitionistic mathematics
03F99 Proof theory and constructive mathematics
03-02 Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations
03F05 Cut-elimination and normal-form theorems
03F30 First-order arithmetic and fragments
03F35 Second- and higher-order arithmetic and fragments

Citations:

Zbl 0439.03041
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