Coverart for item
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

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
Creator
Subject
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 (so-called 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
Member of
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
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages 507-523) 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 -- 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
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
10.1007/978-3-540-77533-1
http://library.link/vocab/ext/overdrive/overdriveId
978-3-540-77532-4
Specific material designation
remote
System control number
(OCoLC)272310282
Label
Applied proof theory : proof interpretations and their use in mathematics, U. Kohlenbach
Publication
Bibliography note
Includes bibliographical references (pages 507-523) 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 -- 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
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
10.1007/978-3-540-77533-1
http://library.link/vocab/ext/overdrive/overdriveId
978-3-540-77532-4
Specific material designation
remote
System control number
(OCoLC)272310282

Library Locations

    • Ellis LibraryBorrow it
      1020 Lowry Street, Columbia, MO, 65201, US
      38.944491 -92.326012
Processing Feedback ...