Diller, Justus (univ Of Munster, Germany) Functional interpretations: from the dialectica interpretation to interpretations of classical and constructive set theory 9789814551397

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Автор: Diller, Justus (univ Of Munster, Germany)
Название: Functional interpretations: from the dialectica interpretation to interpretations of classical and constructive set theory
ISBN: 9789814551397
Издательство: World Scientific Publishing
Классификация:

Математические основы

Математическая логика

ISBN-10: 9814551392
Обложка/Формат: Hardcover
Страницы: 248
Вес: 0.50 кг.
Дата издания: 28.11.2019
Серия: Mathematics
Язык: English
Размер: 236 x 161 x 15
Читательская аудитория: Postgraduate, research & scholarly
Ключевые слова: Mathematical logic, MATHEMATICS / Logic,MATHEMATICS / Set Theory,MATHEMATICS / Functional Analysis
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Поставляется из: Англии
Описание: This book gives a detailed treatment of functional interpretations of arithmetic, analysis, and set theory. The subject goes back to G dels 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, in particular the Dialectica interpretation and its generalization to finite types, the Diller-Nahm interpretation, are studied on Heyting as well as Peano arithmetic in finite types and extended to functional interpretations of constructive as well as classical systems of analysis and set theory. Kreisels modified realization and Troelstras hybrids of it are presented as interpretations of Heyting arithmetic and extended to constructive set theory, both in finite types. They serve as background for the construction of hybrids of the Diller-Nahm interpretation of Heyting arithmetic and constructive set theory, again in finite types. All these functional interpretations yield relative consistency results and closure under relevant rules of the theories in question as well as axiomatic characterizations of the functional translations.

Functional interpretations: from the dialectica interpretation to interpretations of classical and constructive set theory, Diller, Justus (univ Of Munster, Germany)