Applied Proof Theory pdf epub mobi txt 電子書下載2025

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出版者:Springer

作者:Ulrich Kohlenbach

出品人:

頁數:536

译者:

出版時間:2008-5-26

價格:USD 99.00

裝幀:Hardcover

isbn號碼:9783540775324

叢書系列:

圖書標籤:

Math
證明論
nemlophics
Theory
Springer
Proof
MathematicalLogic
邏輯學
證明論
數理邏輯
形式係統
類型論
可計算性理論
數學基礎
邏輯哲學
理論計算機科學
元數學

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具體描述

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.

著者簡介

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".

圖書目錄

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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