Applied proof theory : proof interpretations and their use in mathematics
著者
書誌事項
Applied proof theory : proof interpretations and their use in mathematics
（Springer monographs in mathematics）
Springer, c2010
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注記
Includes bibliographical references (p. [507]-523) and index
内容説明・目次
内容説明
This is the first treatment in book format of proof-theoretic transformations - known as proof interpretations - that focuses on applications to ordinary mathematics. It covers both the necessary logical machinery behind the proof interpretations that are used in recent applications as well as - via extended case studies - carrying out some of these applications in full detail. This subject has historical roots in the 1950s. This book for the first time tells the whole story.
目次
Preface.- Introduction.- Unwinding of proofs (`Proof Mining').- Intuitionistic and classical arithmetic in all finite types.- Representation of Polish metric spaces.- Modified realizability.- Majorizability and the fan rule.- Semi-intuitionistic systems and monotone modified realizability.- Goedel's functional (`Dialectica') interpretation.- Semi-intuitionistic systems and monotone functional interpretation.- Systems based on classical logic and functional interpretation.- Functional interpretation of full classical analysis.- A non-standard principle of uniform boundedness.- Elimination of monotone Skolem functions.- The Friedman-Dragalin A-translation.- Applications to analysis: general metatheorems I.- Case study I: Uniqueness proofs in approximation theory.- Applications to analysis: general metatheorems II.- Case study II: Applications to the fixed point theory of nonexpansive mappings.- Final comments.- References.- Index.
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