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: 9789814551397
Price: 549.42 RON
Availability: InStock

Autor: Justus Diller

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Legare: Copertă tare

Editura: World Scientific Publishing Co Pte Ltd

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

Informații despre carte

Autor

Justus Diller

Limbă

engleză

Legare

Carte - Copertă tare

Publicat

2019

Pagini

248

EAN

9789814551397

ISBN

9814551392

Enbook ID

05071112

Editura

World Scientific Publishing Co Pte Ltd

Greutate

500

Dimensiuni

161 x 236 x 15

Descriere completă

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

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