Functional Interpretations: From the Dialectica Interpretation to Functional Interpretations of Analysis and Set Theory - Rilegato

Libro 2 di 3: Mathematical Logic and Foundat

Diller, Justus

 
9789814551397: Functional Interpretations: From the Dialectica Interpretation to Functional Interpretations of Analysis and Set Theory
Rilegato
ISBN 10: 9814551392 ISBN 13: 9789814551397
Casa editrice: World Scientific Pub Co Inc, 2019

Sinossi

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

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Editore
World Scientific Pub Co Inc
Data di pubblicazione
2019
Lingua
Inglese
ISBN 10 
9814551392
ISBN 13 
9789814551397
Rilegatura
Copertina rigida
Numero di pagine
237
Contatto del produttore
non disponibile
Persona responsabile
non disponibile