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Applied Proof Theory: Proof Interpretations and Their Use in Mathematics: Book by Ulrich Kohlenbach

Applied Proof Theory: Proof Interpretations and Their Use in Mathematics

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ISBN: 9783540775324    Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Year of publishing: 2008     Format:  Hardback Language: English
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...Read more
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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About the author: Ulrich Kohlenbach
Ulrich Kohlenbach has been Professor of Mathematics at the Technische Universitat Darmstadt since 2004. He is a managing editor of the "Annals of Pure... Read more
Ulrich Kohlenbach has been Professor of Mathematics at the Technische Universitat Darmstadt since 2004. He is a managing editor of the "Annals of Pure and Applied Logic".
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Review:
From the reviews: "This book covers ... from proof theory to a rich set of applications in areas quite distinct from mathematical logic: approximation theory and fixed point theory of nonexpansive...Read more
From the reviews: "This book covers ... from proof theory to a rich set of applications in areas quite distinct from mathematical logic: approximation theory and fixed point theory of nonexpansive mappings. ... Almost every chapter has a detailed ... informative final section with exercises, historical comments and references to related work. ... In summary, this book is a very welcome addition to the proof theory literature." (H. Schwichtenberg, Mathematical Reviews, Issue 2009 k)
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