Items related to Applied Proof Theory: Proof Interpretations and their...
Applied Proof Theory: Proof Interpretations and their Use in Mathematics (Springer Monographs in Mathematics) - Softcover
Book 51 of 187: Springer Monographs in Mathematics
Synopsis
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.
"synopsis" may belong to another edition of this title.
About the Author
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".
From the Back Cover
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.
"About this title" may belong to another edition of this title.
Search results for Applied Proof Theory: Proof Interpretations and their...
Stock Image
Applied Proof Theory: Proof Interpretations and their Use in Mathematics (eng)
Print on DemandSeller: Brook Bookstore On Demand, Napoli, NA, Italy
Seller rating 5 out of 5 stars
Condition: new. Questo è un articolo print on demand. Seller Inventory # be320ad0298b174142e19b2f447c5f80
Buy New
£ 97.36
£ 6.86 shipping
Ships from Italy to U.S.A.
Ships from Italy to U.S.A.
Quantity: Over 20 available
Stock Image
Applied Proof Theory: Proof Interpretations and their Use in Mathematics (Springer Monographs in Mathematics)
Seller: Ria Christie Collections, Uxbridge, United Kingdom
Seller rating 5 out of 5 stars
Condition: New. In English. Seller Inventory # ria9783642096273_new
Buy New
£ 96.88
£ 11.29 shipping
Ships from United Kingdom to U.S.A.
Ships from United Kingdom to U.S.A.
Quantity: Over 20 available
Stock Image
Applied Proof Theory: Proof Interpretations and their Use in Mathematics
Seller: Chiron Media, Wallingford, United Kingdom
Seller rating 5 out of 5 stars
PF. Condition: New. Seller Inventory # 6666-IUK-9783642096273
Buy New
£ 95.08
£ 15.49 shipping
Ships from United Kingdom to U.S.A.
Ships from United Kingdom to U.S.A.
Quantity: 10 available
Seller Image
Applied Proof Theory: Proof Interpretations and their Use in Mathematics
Published by
Springer Berlin Heidelberg, Springer Berlin Heidelberg Okt 2010, 2010
ISBN 10: 3642096271
ISBN 13: 9783642096273
New
Taschenbuch
Seller: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germany
Seller rating 5 out of 5 stars
Taschenbuch. Condition: 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 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. 556 pp. Englisch. Seller Inventory # 9783642096273
Seller Image
Applied Proof Theory: Proof Interpretations and their Use in Mathematics
Published by
Springer Berlin Heidelberg, 2010
ISBN 10: 3642096271
ISBN 13: 9783642096273
New
Softcover
Seller: moluna, Greven, Germany
Seller rating 5 out of 5 stars
Condition: 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 . This is the first treatment in book fo. Seller Inventory # 5048631
Buy New
£ 104.73
£ 42 shipping
Ships from Germany to U.S.A.
Ships from Germany to U.S.A.
Quantity: Over 20 available
Stock Image
Applied Proof Theory
Seller: Books Puddle, Woodside, NY, U.S.A.
Seller rating 4 out of 5 stars
Condition: New. pp. 556. Seller Inventory # 262142997
Seller Image
Applied Proof Theory: Proof Interpretations and their Use in Mathematics
Seller: preigu, Osnabrück, Germany
Seller rating 5 out of 5 stars
Taschenbuch. Condition: Neu. Applied Proof Theory: Proof Interpretations and their Use in Mathematics | Ulrich Kohlenbach | Taschenbuch | Springer Monographs in Mathematics | xx | Englisch | 2010 | Springer | EAN 9783642096273 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. Seller Inventory # 107023033
Seller Image
Applied Proof Theory: Proof Interpretations and their Use in Mathematics
Published by
Springer, Springer Vieweg Okt 2010, 2010
ISBN 10: 3642096271
ISBN 13: 9783642096273
New
Taschenbuch
Seller: buchversandmimpf2000, Emtmannsberg, BAYE, Germany
Seller rating 5 out of 5 stars
Taschenbuch. Condition: Neu. This item is printed on demand - Print on Demand Titel. Neuware -Unwinding proofs ('Proof Mining').- Intuitionistic and classical arithmetic in all finite types.- Representation of Polish metric spaces.- Modified realizability.- Majorizability and the fan rule.- Semi-intuitionistic systems and monotone modified realizability.- Gödel's functional ('Dialectica') interpretation.- Semi-intuitionistic systems and monotone functional interpretation.- Systems based on classical logic and functional interpretation.- Functional interpretation of full classical analysis.- A non-standard principle of uniform boundedness.- Elimination of monotone Skolem functions.- The Friedman A-translation.- Applications to analysis: general metatheorems I.- Case study I: Uniqueness proofs in approximation theory.- Applications to analysis: general metatheorems II.- Case study II: Applications to the fixed point theory of nonexpansive mappings.- Final comments.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 556 pp. Englisch. Seller Inventory # 9783642096273
Stock Image
Applied Proof Theory
Print on DemandSeller: Majestic Books, Hounslow, United Kingdom
Seller rating 4 out of 5 stars
Condition: New. Print on Demand pp. 556 49:B&W 6.14 x 9.21 in or 234 x 156 mm (Royal 8vo) Perfect Bound on White w/Gloss Lam. Seller Inventory # 5704906
Buy New
£ 169.34
£ 6.50 shipping
Ships from United Kingdom to U.S.A.
Ships from United Kingdom to U.S.A.
Quantity: 4 available
Stock Image
Applied Proof Theory
Print on DemandSeller: Biblios, Frankfurt am main, HESSE, Germany
Seller rating 4 out of 5 stars
Condition: New. PRINT ON DEMAND pp. 556. Seller Inventory # 182143007