Applied Proof Theory: Proof Interpretations and their Use in Mathematics - Couverture souple

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Kohlenbach, Ulrich

9783642096273: Applied Proof Theory: Proof Interpretations and their Use in Mathematics

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ISBN 10 : 3642096271 ISBN 13 : 9783642096273

Editeur : Springer, 2010

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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.

Les informations fournies dans la section � Synopsis � peuvent faire r�f�rence � une autre �dition de ce titre.

� propos de l?auteur

Ulrich Kohlenbach has been Professor of Mathematics at the Technische Universit�t Darmstadt since 2004. He is a managing editor of the "Annals of Pure and Applied Logic".

Les informations fournies dans la section � A propos du livre � peuvent faire r�f�rence � une autre �dition de ce titre.

�diteur: Springer
Date d'�dition: 2010
Langue: anglais
ISBN 10: 3642096271
ISBN 13: 9783642096273
Reliure: Broch�
Num�ro d'�dition: 1
Nombre de pages: 556
Coordonn�es du fabricant: non disponible
Personne responsable: CMN Printpool Inh. Mathis Neumann
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Applied Proof Theory: Proof Interpretations and their Use in Mathematics (eng)

Kohlenbach, Ulrich

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

Kohlenbach, Ulrich

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ISBN 10 : 3642096271 ISBN 13 : 9783642096273

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Applied Proof Theory: Proof Interpretations and their Use in Mathematics

Kohlenbach, Ulrich

Edit� par Springer 2010-10, 2010

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Applied Proof Theory: Proof Interpretations and their Use in Mathematics

Ulrich Kohlenbach

Edit� par Springer Berlin Heidelberg, Springer Berlin Heidelberg Okt 2010, 2010

ISBN 10 : 3642096271 ISBN 13 : 9783642096273

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Taschenbuch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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 G�del'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. 556 pp. Englisch. N� de r�f. du vendeur 9783642096273

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Applied Proof Theory: Proof Interpretations and their Use in Mathematics

Ulrich Kohlenbach

Edit� par Springer Berlin Heidelberg, 2010

ISBN 10 : 3642096271 ISBN 13 : 9783642096273

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Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. First book on the subject at allUlrich Kohlenbach has been Professor of Mathematics at the Technische Universitaet Darmstadt since 2004. He is a managing editor of the Annals of Pure and Applied Logic .&nbspThis is the first treatment in book fo. N� de r�f. du vendeur 5048631

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Applied Proof Theory: Proof Interpretations and their Use in Mathematics

Ulrich Kohlenbach

Edit� par Springer, 2010

ISBN 10 : 3642096271 ISBN 13 : 9783642096273

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Applied Proof Theory: Proof Interpretations and their Use in Mathematics

Ulrich Kohlenbach

Edit� par Springer Berlin Heidelberg, Springer Berlin Heidelberg Okt 2010, 2010

ISBN 10 : 3642096271 ISBN 13 : 9783642096273

Neuf Taschenbuch

Vendeur : buchversandmimpf2000, Emtmannsberg, BAYE, Allemagne

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Taschenbuch. Etat : Neu. Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 556 pp. Englisch. N� de r�f. du vendeur 9783642096273

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Applied Proof Theory: Proof Interpretations and their Use in Mathematics

Ulrich Kohlenbach

Edit� par Springer Berlin Heidelberg, 2010

ISBN 10 : 3642096271 ISBN 13 : 9783642096273

Neuf Taschenbuch

Vendeur : AHA-BUCH GmbH, Einbeck, Allemagne

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Taschenbuch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - 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 G�del'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. N� de r�f. du vendeur 9783642096273

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