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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. …mehr

Produktbeschreibung
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.
  • Produktdetails
  • Springer Monographs in Mathematics
  • Verlag: Springer, Berlin
  • Artikelnr. des Verlages: 12029426
  • 2008
  • Seitenzahl: 556
  • Erscheinungstermin: 26. Mai 2008
  • Englisch
  • Abmessung: 241mm x 160mm x 34mm
  • Gewicht: 960g
  • ISBN-13: 9783540775324
  • ISBN-10: 3540775323
  • Artikelnr.: 23466511
Autorenporträt
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".
Inhaltsangabe
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.

Rezensionen
From the reviews:

"This book covers ... from proof theory to a rich set of applications in areas quite distinct from mathematical logic: approximation theory and fixed point theory of nonexpansive mappings. ... Almost every chapter has a detailed ... informative final section with exercises, historical comments and references to related work. ... In summary, this book is a very welcome addition to the proof theory literature." (H. Schwichtenberg, Mathematical Reviews, Issue 2009 k)