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More about Functional Interpretations: From The Dialectica Interpretation To Functional Interpretations Of Analysis And Set Theory

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Book synopsis

This book gives a detailed treatment of functional interpretations of arithmetic, analysis, and set theory. The subject goes back to Godel'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, i.e. Dialectica and Diller - Nahm interpretation as well as Kreisel's modified realization, together with their Troelstra-style hybrids, are applied to constructive as well as classical systems of arithmetic, analysis, and set theory. They yield relative consistency and conservativity results and closure under relevant rules of the theories in question as well as axiomatic characterizations of the functional translations. Prerequisites are: familiarity with classical and intuitionistic predicate logic, basics of computability theory, Godel's incompleteness theorems.

Book details

Book category Books in English Mathematics & science Mathematics Mathematical foundations

• Full title: Functional Interpretations: From The Dialectica Interpretation To Functional Interpretations Of Analysis And Set Theory
• Author: Justus Diller
• Language: English
• Binding: Hardback
• Number of pages: 248
• EAN: 9789814551397
• ISBN: 9814551392
• ID: 05071112
• Publisher: World Scientific Publishing Co Pte Ltd
• Weight: 500 g
• Dimensions: 236 × 161 × 15 mm
• Date of publishing: 28. November 2019

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