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Applied Proof Theory: Proof Interpretations and their Use in Mathematics (Springer Monographs in Mathematics) - Hardcover

Buch 51 von 187: Springer Monographs in Mathematics

Kohlenbach, Ulrich

 
9783540775324: Applied Proof Theory: Proof Interpretations and their Use in Mathematics (Springer Monographs in Mathematics)
Hardcover
ISBN 10: 3540775323 ISBN 13: 9783540775324
Verlag: Springer, 2008

Inhaltsangabe

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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Über die Autorin bzw. den Autor

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". 

Von der hinteren Coverseite

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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Verlag
Springer
Erscheinungsdatum
2008
Sprache
Englisch
ISBN 10 
3540775323
ISBN 13 
9783540775324
Einband
Gebundene Ausgabe
Anzahl der Seiten
556
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