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Books in English > Mathematics & Science > Mathematics > Mathematical foundations > Mathematical logic > Functional Interpretations: From The Dialectica Interpretation To Functional Interpretations Of Analysis And Set Theory

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 Co Pte Ltd
SKU: 05071112
Price: 106.59 EUR
Availability: InStock
Author: Justus Diller
ISBN: 9789814551397

Justus Diller

Language

English

Book Hardback

Libristo code: 05071112

Publishers World Scientific Publishing Co Pte Ltd, November 2019

This book gives a detailed treatment of functional interpretations of arithmetic, analysis, and set... Full description

Libristo code: 05071112

261 b

106.59 € VAT included

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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.