Applied proof theory : proof interpretations and their use in mathematics
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The work Applied proof theory : proof interpretations and their use in mathematics represents a distinct intellectual or artistic creation found in University of Missouri Libraries. This resource is a combination of several types including: Work, Language Material, Books.
The Resource
Applied proof theory : proof interpretations and their use in mathematics
Resource Information
The work Applied proof theory : proof interpretations and their use in mathematics represents a distinct intellectual or artistic creation found in University of Missouri Libraries. This resource is a combination of several types including: Work, Language Material, Books.
 Label
 Applied proof theory : proof interpretations and their use in mathematics
 Title remainder
 proof interpretations and their use in mathematics
 Statement of responsibility
 U. Kohlenbach
 Subject

 31.10 logic, set theory
 31.46 functional analysis
 31.46 functional analysis
 Approximation theory
 Approximation theory
 Approximation theory
 Approximation theory
 Automatic theorem proving
 Automatic theorem proving
 Automatic theorem proving
 Automatic theorem proving
 MATHEMATICS  Infinity
 MATHEMATICS  Logic
 Nonlinear operators
 Nonlinear operators
 Nonlinear operators
 Nonlinear operators
 Proof theory
 Proof theory
 Proof theory
 Proof theory
 31.10 logic, set theory
 Language
 eng
 Summary
 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 (socalled 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
 Cataloging source
 GW5XE
 Dewey number
 511.3/6
 Index
 index present
 LC call number
 QA9.54
 LC item number
 .K64 2008eb
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 Springer monographs in mathematics
Context
Context of Applied proof theory : proof interpretations and their use in mathematicsWork of
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