Set theory for the working mathematician /

This text presents methods of modern set theory as tools that can be usefully applied to other areas of mathematics. The author describes numerous applications in abstract geometry and real analysis and, in some cases, in topology and algebra. The book begins with a tour of the basics of set theory,...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Ciesielski, Krzysztof, 1957-
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge ; New York : Cambridge University Press, ©1997.
Colección:London Mathematical Society student texts ; 39.
Temas:
Set theory.
Théorie des ensembles.
MATHEMATICS > Set Theory.
Set theory
Mengenlehre
TEORIA DOS CONJUNTOS.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Basics of set theory
  • Axiomatic set theory
  • Why axiomatic set theory?
  • The language and the basic axioms
  • Relations, functions, and Cartesian product
  • Relations and the axiom of choice
  • Functions and the replacement scheme axiom
  • Generalized union, intersection, and Cartesian product
  • Partial- and linear-order relations
  • Natural numbers, integers, and real numbers
  • Natural numbers
  • Integers and rational numbers
  • Real numbers
  • Fundamental tools of set theory
  • Well orderings and transfinite induction
  • Well-ordered sets and the axiom of foundation
  • Ordinal numbers
  • Definitions by transfinite induction
  • Zorn's lemma in algebra, analysis, and topology
  • Cardinal numbers
  • Cardinal numbers and the continuum hypothesis
  • Cardinal arithmetic
  • Cofinality
  • The power of recursive definitions
  • Subsets of R[superscript n]
  • Strange subsets of R[superscript n] and the diagonalization argument
  • Closed sets and Borel sets
  • Lebesgue-measurable sets and sets with the Baire property
  • Strange real functions
  • Measurable and nonmeasurable functions
  • Darboux functions
  • Additive functions and Hamel bases
  • Symmetrically discontinuous functions
  • When induction is too short
  • Martin's axiom
  • Rasiowa-Sikorski lemma
  • Martin's axiom
  • Suslin hypothesis and diamond principle
  • Forcing
  • Elements of logic and other forcing preliminaries
  • Forcing method and a model for [not sign]CH
  • Model for CH and [diamonds suit symbol]
  • Product lemma and Cohen model
  • Model for MA+[not sign]CH.

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