Functional Interpretations: From The Dialectica Interpretation To Functional Interpretations Of Analysis And Set Theory (Mathematical Logic and Foundat)

Enjoying reading this book?

Functional Interpretations: From The Dialectica Interpretation To Functional Interpretations Of Analysis And Set Theory (Mathematical Logic and Foundat)

Name: Functional Interpretations: From The Dialectica Interpretation To Functional Interpretations Of Analysis And Set Theory (Mathematical Logic and Foundat)
Availability: in stock
Rating: 4.9 (26 reviews)
Author: Justus Diller
ISBN: 9789814551397

by Justus Diller

4.9

4.9 out of 5

Creators

Author Justus Diller

Publisher World Scientific Publishing Co Pte Ltd

Synopsis This book gives a detailed treatment of functional interpretations of arithmetic, analysis, and set theory. The subject goes back to G del'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, G del's incompleteness theorems.

Enjoying reading this book?

Binding: Hardcover

About the author

Specifications

Language: English
Publisher: World Scientific Publishing Co Pte Ltd
Pages: 248 pages
Binding: Hardcover

ISBN: 9789814551397
Category: Mathematics & logic
Related Category: Natural Sciences