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: 9783540775324
Price: 716.32 RON
Availability: InStock

Proof Interpretations and their Use in Mathematics

Autor: Ulrich Kohlenbach

Limbă:

Legare: Copertă tare

Editura: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

Disponibilitate: În depozitul extern

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716.32 lei

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

Informații despre carte

Autor

Ulrich Kohlenbach

Limbă

engleză

Legare

Carte - Copertă tare

Publicat

2008

Pagini

536

EAN

9783540775324

ISBN

3540775323

Enbook ID

02108106

Editura

Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

Greutate

940

Dimensiuni

164 x 237 x 36

Descriere completă

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.

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Applied Proof Theory: Proof Interpretations and their Use in Mathematics

Proof Interpretations and their Use in Mathematics

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Descriere completă

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