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Set theory /

This is a classic introduction to set theory in three parts. The first part gives a general introduction to set theory, suitable for undergraduates; complete proofs are given and no background in logic is required. Exercises are included, and the more difficult ones are supplied with hints. An appen...

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Bibliographic Details
Call Number:Libro Electrónico
Main Author: Hajnal, A.
Other Authors: Hamburg, P.
Format: Electronic eBook
Language:Inglés
Hungarian
Published: Cambridge ; New York : Cambridge University Press, 1999.
Edition:1st English ed.
Series:London Mathematical Society student texts ; 48.
Subjects:
Online Access:Texto completo
Table of Contents:
  • Definition of equivalence. The concept of cardinality. The Axiom of Choice
  • Countable cardinal, continuum cardinal
  • Comparison of cardinals
  • Operations with sets and cardinals
  • Ordered sets. Order types. Ordinals
  • Properties of wellordered sets. Good sets. The ordinal operation
  • Transfinite induction and recursion. Some consequences of the Axiom of Choice, the Wellordering Theorem
  • Definition of the cardinality operation. Properties of cardinalities. The cofinality operation
  • Properties of the power operation
  • Hints for solving problems marked with * in Part I
  • An axiomatic development of set theory
  • The Zermelo-Fraenkel axiom system of set theory
  • Definition of concepts; extension of the language
  • A sketch of the development. Metatheorems
  • A sketch of the development. Definitions of simple operations and properties (continued)
  • A sketch of the development. Basic theorems, the introduction of [omega] and R (continued)
  • The ZFC axiom system. A weakening of the Axiom of Choice. Remarks on the theorems of Sections 2-7
  • The role of the Axiom of Regularity
  • Proofs of relative consistency. The method of interpretation
  • Proofs of relative consistency. The method of models
  • Topics in combinatorial set theory
  • Stationary sets
  • [Delta]-systems
  • Ramsey's Theorem and its generalizations. Partition calculus
  • Inaccessible cardinals. Mahlo cardinals
  • Measurable cardinals
  • Real-valued measurable cardinals, saturated ideals
  • Weakly compact and Ramsey cardinals
  • Set mappings.