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Applied Proof Theory: Proof Interpretations and their Use in Mathematics (Springer Monographs in Mathematics) [Hardcover]

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Item description for Applied Proof Theory: Proof Interpretations and their Use in Mathematics (Springer Monographs in Mathematics) by U. Kohlenbach...

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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Item Specifications...


Pages   536
Est. Packaging Dimensions:   Length: 9.45" Width: 6.46" Height: 1.34"
Weight:   2.2 lbs.
Binding  Hardcover
Release Date   May 27, 2008
Publisher   Springer
ISBN  3540775323  
ISBN13  9783540775324  


Availability  122 units.
Availability accurate as of Jan 17, 2017 06:08.
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Product Categories

1Books > Special Features > New & Used Textbooks > Sciences > Mathematics > Algebra & Trigonometry
2Books > Subjects > Professional & Technical > Professional Science > Mathematics > Mathematical Analysis
3Books > Subjects > Professional & Technical > Professional Science > Mathematics > Pure Mathematics > Functional Analysis
4Books > Subjects > Professional & Technical > Professional Science > Mathematics > Pure Mathematics > Logic
5Books > Subjects > Professional & Technical > Professional Science > Mathematics > Pure Mathematics > Number Theory
6Books > Subjects > Science > General
7Books > Subjects > Science > Mathematics > General
8Books > Subjects > Science > Mathematics > Mathematical Analysis
9Books > Subjects > Science > Mathematics > Pure Mathematics > Algebra > Intermediate
10Books > Subjects > Science > Mathematics > Pure Mathematics > Functional Analysis
11Books > Subjects > Science > Mathematics > Pure Mathematics > Logic
12Books > Subjects > Science > Mathematics > Pure Mathematics > Number Theory



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