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Author:  U. Kohlenbach
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Applied Proof Theory: Proof Interpretations and Their Use in Mathematics Kohlenbach, U. 1 of 1
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FORMAT: Hardcover
CONDITION:  Brand New
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Description
 

Product Details:

Format: Hardcover
ISBN-10: 3540775323
ISBN-13: 9783540775324
Sku: 207532884
Publish Date: 6/1/2008
Dimensions:  (in Inches) 9.75H x 6.75L x 1.25T
Pages:  532
Age Range:  NA
See more in Logic
 

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.

From the Publisher:
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 - carries out some of these applications in full detail. This subject has its historical roots in pioneering work of G. Kreisel going back to the 1950s but was developed more systematically only during the past 15-20 years, mainly by the author and his collaborators in numerous paper. The main direction in this work is to apply proof transformations that originally had been developed in the course of foundational studies (erg. consistency proofs and Hilbert's program) as well as new versions and extensions thereof to concrete pieces of mathematics. This work so far only existed in the form of research papers that either developed the logical machinery and were published in logic journals or that presented concrete applications (mainly in analysis) and were published in analysis journals on the expense of dropping most of the logical background. The present book for the first time tells the whole story: the logical theory, how to connect this theory up with ordinary mathematics and, finally, concrete applications in approximation theory and fixed point theory.
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