Applied Proof Theory: Proof Interpretations and Their Use in Mathematics

By Ulrich Kohlenbach

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.- G del'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.

• Format: Paperback
• Language: English
• ISBN: 3642096271
• ISBN13: 9783642096273
• Release Date: October 2010
• Publisher: Springer
• Length: 536 Pages
• Weight: 1.70 lbs.
• Dimensions: 1.1" x 6.1" x 9.2"