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

Language EnglishEnglish
Book Hardback
Book Functional Interpretations: From The Dialectica Interpretation To Functional Interpretations Of Analysis And Set Theory Justus Diller
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
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103.53 €
202.49  лв
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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.

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About the book

Full name Functional Interpretations: From The Dialectica Interpretation To Functional Interpretations Of Analysis And Set Theory
Author Justus Diller
Language English
Binding Book - Hardback
Date of issue 2019
Number of pages 248
EAN 9789814551397
ISBN 9814551392
Libristo code 05071112
Publishers World Scientific Publishing Co Pte Ltd
Weight 500
Dimensions 161 x 236 x 15

Categories

Mathematics & Science > Mathematics > Mathematical foundations > Mathematical logic
Mathematics & Science > Mathematics > Mathematical foundations > Set theory
Mathematics & Science > Mathematics > Calculus & mathematical analysis > Functional analysis & transforms
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