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: 425.81 PLN
Availability: InStock

Autor: Justus Diller

Język:

Oprawa: Twarda

Wydawca: World Scientific Publishing Co Pte Ltd

Dostępność: Dostępna u dostawcy

Wysyłamy za 9-15 dni

425.81 zł

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

Informacje o książce

Autor

Justus Diller

Język

Angielski

Oprawa

Książka - Twarda

Data wydania

2019

strony

248

EAN

9789814551397

ISBN

9814551392

Enbook ID

05071112

Wydawca

World Scientific Publishing Co Pte Ltd

Waga

500

Wymiary

161 x 236 x 15

Pełny opis

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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