Ulrich Kohlenbach
Springer Berlin Heidelberg
2008e druk, 2008
9783540775324
Applied Proof Theory: Proof Interpretations and their Use in Mathematics
Specificaties
Gebonden, 536 blz.
|
Engels
Springer Berlin Heidelberg |
2008e druk, 2008
ISBN13: 9783540775324
Rubricering
Onderdeel van serie
Springer Monographs in Mathematics
Levertijd ongeveer 8 werkdagen
Samenvatting
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.
Specificaties
ISBN13:9783540775324
Taal:Engels
Bindwijze:gebonden
Aantal pagina's:536
Uitgever:Springer Berlin Heidelberg
Druk:2008
Inhoudsopgave
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.