Ulrich Kohlenbach

Applied Proof Theory: Proof Interpretations and their Use in Mathematics (eBook, PDF)

• Format: PDF

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.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 536
• Erscheinungstermin: 23. Mai 2008
• Englisch
• ISBN-13: 9783540775331
• Artikelnr.: 37370581

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

Unwinding 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 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.

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)