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Applied Proof Theory: Proof Interpretations and Their Use in Mathematics

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Cover of 'Applied Proof Theory: Proof Interpretations and Their Use in Mathematics'

Table of Contents

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    Book Overview
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    Chapter 1 Introduction
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    Chapter 2 Unwinding proofs (‘Proof Mining’)
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    Chapter 3 Intuitionistic and classical arithmetic in all finite types
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    Chapter 4 Representation of Polish metric spaces
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    Chapter 5 Modified realizability
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    Chapter 6 Majorizability and the fan rule
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    Chapter 7 Semi-intuitionistic systems and monotone modified realizability
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    Chapter 8 Gödel’s functional (‘Dialectica’) interpretation
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    Chapter 9 Semi-intuitionistic systems and monotone functional interpretation
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    Chapter 10 Systems based on classical logic and functional interpretation
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    Chapter 11 Functional interpretation of full classical analysis
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    Chapter 12 A non-standard principle of uniform boundedness
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    Chapter 13 Elimination of monotone Skolem functions
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    Chapter 14 The Friedman A -translation
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    Chapter 15 Applications to analysis: general metatheorems I
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    Chapter 16 Case study I: Uniqueness proofs in approximation theory
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    Chapter 17 Applications to analysis: general metatheorems II
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    Chapter 18 Case study II: Applications to the fixed point theory of nonexpansive mappings
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    Chapter 19 Final comments
Attention for Chapter 12: A non-standard principle of uniform boundedness
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