Kohlenbach Applied Proof Theory: Proof Interpretations and their Use in Mathematics

1. Auflage 2008
ISBN: 978-3-540-77533-1
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 536 Seiten, eBook

Reihe: Springer Monographs in Mathematics

Zielgruppe

Research

Autoren/Hrsg.

Kohlenbach, Ulrich

Inhaltsverzeichnis

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.

Über Autor(innen)

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".