Applied Proof Theory: Proof Interpretations and their Use in Mathematics

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 interpret...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Kohlenbach, Ulrich (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2008.
Edición:1st ed. 2008.
Colección:Springer Monographs in Mathematics,
Temas:
Mathematical logic.
Mathematics.
Approximation theory.
Operator theory.
Functional analysis.
Mathematical Logic and Foundations.
Approximations and Expansions.
Operator Theory.
Functional Analysis.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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.

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