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Applied Proof Theory: Proof Interpretations and their Use in Mathematics: Kohlenbach by Ulrich Kohlenbach (auth.) is a nonfiction available to read on EtoBox.

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Ulrich Kohlenbach presents an applied form of proof theory that has led in recent years to new results in number theory, approximation theory, nonlinear analysis, geodesic geometry and ergodic theory (among others). 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 such as independence of solutions from certain parameters, generalizations of proofs by elimination of premises. 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.

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Author

Ulrich Kohlenbach (auth.)

Publisher

Springer Berlin

Published

2008

Language

EN

ISBN

9783540775331

Category

nonfiction

Subjects

Mathematics, Stem