Descriptive set theory and forcing : how to prove theorems about borel sets the hard way /

These notes develop the theory of descriptive sets, leading up to a new proof of Louveau's separation theorem for analytic sets.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Miller, Arnold W., 1950- (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge : Cambridge University Press, 2017.
Colección:Lecture notes in logic ; 4.
Temas:
Set theory.
Forcing (Model theory)
Borel sets.
Théorie des ensembles.
Forcing (Théorie des modèles)
Ensembles boréliens.
MATHEMATICS > General.
Borel sets
Set theory
Acceso en línea:Texto completo
Tabla de Contenidos:
  • I
  • On the length of Borel hierarchies
  • Borel Hierarchy
  • Abstract Borel hierarchies
  • Characteristic function of a sequence
  • Martin's Axiom
  • Generic G[textdelta]
  • [textalpha]-forcing
  • Boolean algebras
  • Borel order of a field of sets
  • CH and orders of separable metric spaces
  • Martin-Solovay Theorem
  • Boolean algebra of order [textomega]
  • Luzin sets
  • Cohen real model
  • The random real model
  • Covering number of an ideal
  • II
  • Analytic sets
  • Analytic sets
  • Constructible well-orderings
  • Hereditarily countable sets
  • Shoenfield Absoluteness
  • Mansfield-Solovay Theorem
  • Uniformity and Scales
  • Martin's axiom and Constructibility
  • well-orderings
  • Large sets
  • III
  • Classical Separation Theorems
  • Souslin-Luzin Separation Theorem
  • Kleene Separation Theorem
  • -Reduction
  • -codes
  • IV
  • Gandy Forcing
  • equivalence relations
  • Borel metric spaces and lines in the plane
  • equivalence relations
  • Louveau's Theorem
  • Proof of Louveau's Theorem.

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