The Resource Applied proof theory : proof interpretations and their use in mathematics, U. Kohlenbach
Applied proof theory : proof interpretations and their use in mathematics, U. Kohlenbach
Resource Information
The item Applied proof theory : proof interpretations and their use in mathematics, U. Kohlenbach represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Applied proof theory : proof interpretations and their use in mathematics, U. Kohlenbach represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 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
 Language
 eng
 Extent
 1 online resource (xix, 532 pages).
 Contents

 Unwinding proofs ('Proof Mining')
 Intuitionistic and classical arithmetic in all finite types
 Representation of Polish metric spaces
 Modified realizability
 Majorizability and the fan rule
 Semiintuitionistic systems and monotone modified realizability
 Gödel's functional ('Dialectica') interpretation
 Semiintuitionistic systems and monotone functional interpretation
 Systems based on classical logic and functional interpretation
 Functional interpretation of full classical analysis
 A nonstandard principle of uniform boundedness
 Elimination of monotone Skolem functions
 The Friedman Atranslation
 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
 Isbn
 9783540775324
 Label
 Applied proof theory : proof interpretations and their use in mathematics
 Title
 Applied proof theory
 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
 http://library.link/vocab/creatorName
 Kohlenbach, U.
 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
 http://library.link/vocab/subjectName

 Proof theory
 Approximation theory
 Nonlinear operators
 Automatic theorem proving
 31.10 logic, set theory
 31.46 functional analysis
 MATHEMATICS
 MATHEMATICS
 Approximation theory
 Nonlinear operators
 Automatic theorem proving
 Proof theory
 Approximation theory
 Automatic theorem proving
 Nonlinear operators
 Proof theory
 Label
 Applied proof theory : proof interpretations and their use in mathematics, U. Kohlenbach
 Bibliography note
 Includes bibliographical references (pages 507523) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Unwinding proofs ('Proof Mining')  Intuitionistic and classical arithmetic in all finite types  Representation of Polish metric spaces  Modified realizability  Majorizability and the fan rule  Semiintuitionistic systems and monotone modified realizability  Gödel's functional ('Dialectica') interpretation  Semiintuitionistic systems and monotone functional interpretation  Systems based on classical logic and functional interpretation  Functional interpretation of full classical analysis  A nonstandard principle of uniform boundedness  Elimination of monotone Skolem functions  The Friedman Atranslation  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
 Control code
 272310282
 Dimensions
 unknown
 Extent
 1 online resource (xix, 532 pages).
 Form of item
 online
 Isbn
 9783540775324
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783540775331
 http://library.link/vocab/ext/overdrive/overdriveId
 9783540775324
 Specific material designation
 remote
 System control number
 (OCoLC)272310282
 Label
 Applied proof theory : proof interpretations and their use in mathematics, U. Kohlenbach
 Bibliography note
 Includes bibliographical references (pages 507523) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Unwinding proofs ('Proof Mining')  Intuitionistic and classical arithmetic in all finite types  Representation of Polish metric spaces  Modified realizability  Majorizability and the fan rule  Semiintuitionistic systems and monotone modified realizability  Gödel's functional ('Dialectica') interpretation  Semiintuitionistic systems and monotone functional interpretation  Systems based on classical logic and functional interpretation  Functional interpretation of full classical analysis  A nonstandard principle of uniform boundedness  Elimination of monotone Skolem functions  The Friedman Atranslation  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
 Control code
 272310282
 Dimensions
 unknown
 Extent
 1 online resource (xix, 532 pages).
 Form of item
 online
 Isbn
 9783540775324
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783540775331
 http://library.link/vocab/ext/overdrive/overdriveId
 9783540775324
 Specific material designation
 remote
 System control number
 (OCoLC)272310282
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
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