Applied Proof Theory: Proof Interpretations and their Use in Mathematics
Published on 21. October 2010
Book
Paperback/Softback
XX, 536 pages
978-3-642-09627-3 (ISBN)
Description
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 / Votes
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)
More details
Series
Edition
1st ed. Softcover of orig. ed. 2008
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
XX, 536 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 30 mm
Weight
832 gr
ISBN-13
978-3-642-09627-3 (9783642096273)
DOI
10.1007/978-3-540-77533-1
Schweitzer Classification
Other editions
Additional editions
Ulrich Kohlenbach
Applied Proof Theory: Proof Interpretations and their Use in Mathematics
Book
05/2008
Springer
€139.09
Shipment within 10-15 days
Person
Ulrich 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".
Content
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.