Functional Interpretations: From the Dialectica Interpretation to Functional Interpretations of Analysis and Set Theory - Image 1

£80.99

World Scientific Publishing Company Functional Interpretations: From the Dialectica Interpretation to Functional Interpretations of Analysis and Set Theory

Name: Functional Interpretations: From the Dialectica Interpretation to Functional Interpretations of Analysis and Set Theory
Brand: World Scientific Publishing Company
Price: 78.19 GBP
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This book gives a detailed treatment of functional interpretations of arithmetic, analysis, and set theory. The subject goes back to Gödel's Dialectica interpretation of Heyting arithmetic which replaces nested quantification by higher type operations and thus reduces the consistency problem for arithmetic to the problem of computability of primitive recursive functionals of finite types. Regular functional interpretations, in particular the Dialectica interpretation and its generalization to finite types, the Diller-Nahm interpretation, are studied on Heyting as well as Peano arithmetic in finite types and extended to functional interpretations of constructive as well as classical systems of analysis and set theory. Kreisel's modified realization and Troelstra's hybrids of it are presented as interpretations of Heyting arithmetic and extended to constructive set theory, both in finite types. They serve as background for the construction of hybrids of the Diller-Nahm interpretation of Heyting arithmetic and constructive set theory, again in finite types. All these functional interpretations yield relative consistency results and closure under relevant rules of the theories in question as well as axiomatic characterizations of the functional translations.

Product Specifications

Brand: World Scientific Publishing Company
Format: hardcover
ASIN: 9814551392
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Mathematical Analysis > Functional Analysis
Domain: Amazon UK
Release Date: 28 February 2017
Listed Since: 27 June 2014

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World Scientific Publishing Company Functional Interpretations: From the Dialectica Interpretation to Functional Interpretations of Analysis and Set Theory

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