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Functional Interpretations : From the Dialectica Interpretation to Interpretations of Classical and

Functional Interpretations : From the Dialectica Interpretation to Interpretations of Classical and - image 1 of 1

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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.
Number of Pages: 250
Genre: Mathematics
Format: Hardcover
Publisher: World Scientific Pub Co Inc
Author: Justus Diller
Language: English
Street Date: May 31, 2018
TCIN: 53908559
UPC: 9789814551397
Item Number (DPCI): 248-09-1833
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$86.53
MSRPReg: $98.00 Save $11.47 (12% off)
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