Applied Proof Theory: Proof Interpretations and their Use in Mathematics - Springer Monographs in Mathematics (Hardback)Ulrich Kohlenbach (author)
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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.
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Number of pages: 536
Weight: 2100 g
Dimensions: 235 x 155 x 30 mm
Edition: 2008 ed.
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)