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Springer Monographs in Mathematics

Applied Proof Theory: Proof Interpretations and their Use in Mathematics

Authors: Kohlenbach, Ulrich

  • First book on the subject
  • Tells the whole story
  • Extended case studies
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eBook $74.99
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  • ISBN 978-3-540-77533-1
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  • Included format: PDF
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  • Immediate eBook download after purchase
Hardcover $99.00
price for USA
  • ISBN 978-3-540-77532-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $99.00
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  • ISBN 978-3-642-09627-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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 the authors

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". 

Reviews

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)


Table of contents (19 chapters)

Buy this book

eBook $74.99
price for USA
  • ISBN 978-3-540-77533-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.00
price for USA
  • ISBN 978-3-540-77532-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $99.00
price for USA
  • ISBN 978-3-642-09627-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Applied Proof Theory: Proof Interpretations and their Use in Mathematics
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2008
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-77533-1
DOI
10.1007/978-3-540-77533-1
Hardcover ISBN
978-3-540-77532-4
Softcover ISBN
978-3-642-09627-3
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XX, 536
Topics