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Applied Proof Theory: Proof Interpretations and their Use in Mathematics

Name: Applied Proof Theory: Proof Interpretations and their Use in Mathematics
Brand: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
SKU: 02108106
Price: 132.29 EUR
Availability: InStock
Author: Ulrich Kohlenbach
ISBN: 9783540775324

Proof Interpretations and their Use in Mathematics

Ulrich Kohlenbach

Language

English

Book Hardback

Libristo code: 02108106

Publishers Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, May 2008

This book presents an applied form of proof theory that has led to new results in number theory, app... Full description

Libristo code: 02108106

324 b

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This book presents an applied form of proof theory that has led to new results in number theory, approximation theory, nonlinear analysis, geodesic geometry and ergodic theory (among others) in recent years . This applied approach is based on logical transformations (so-called proof interpretations) and concerns the extraction of effective data (such as bounds) from prima facie ineffective proofs as well as new qualitative results (independence of solutions from certain parameters, generalizations of proofs by elimination of premises and others). §The book first develops the necessary logical machinery emphasizing novel forms of Gödel's famous functional ('Dialectica') interpretation. It then establishes general logical metatheorems that connect these techniques with concrete mathematics. Finally, two extended case studies (one in approximation theory and one in fixed point theory) show in detail how this machinery can be applied to concrete proofs in different areas of mathematics.