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Applied Proof Theory: Proof Interpretations and Their Use in Mathematics

Applied Proof Theory: Proof Interpretations and Their Use in Mathematics

Paperback

Series: Springer Monographs in Mathematics

FictionGeneral Mathematics

ISBN10: 3642096271
ISBN13: 9783642096273
Publisher: Springer Nature
Published: Oct 21 2010
Pages: 536
Weight: 1.70
Height: 1.13 Width: 6.14 Depth: 9.21
Language: English
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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