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出版者:Springer

作者:Ulrich Kohlenbach

出品人:

页数:536

译者:

出版时间:2008-5-26

价格:USD 99.00

装帧:Hardcover

isbn号码:9783540775324

丛书系列:

图书标签:

Math
证明论
nemlophics
Theory
Springer
Proof
MathematicalLogic
逻辑学
证明论
数理逻辑
形式系统
类型论
可计算性理论
数学基础
逻辑哲学
理论计算机科学
元数学

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具体描述

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.

作者简介

Ulrich Kohlenbach has been Professor of Mathematics at the Technische Universität Darmstadt since 2004. He is a managing editor of the "Annals of Pure and Applied Logic".

目录信息

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.- Gödel'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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