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Set theory

Author: A Hajnal; P Hamburg
Publisher: Cambridge ; New York : Cambridge University Press, 1999.
Series: London Mathematical Society student texts, 48.
Edition/Format:   Print book : English : 1st English edView all editions and formats
Summary:

This is a classic introduction to set theory, from the basics through to the modern tools of combinatorial set theory.

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: A Hajnal; P Hamburg
ISBN: 0521593441 9780521593441 052159667X 9780521596671
OCLC Number: 41143004
Language Note: Translated into English.
Notes: Originally published in Hungarian as Halmazeimélet, 1983.
Description: viii, 316 pages ; 24 cm.
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.
Series Title: London Mathematical Society student texts, 48.
Other Titles: Halmazeimélet.
Responsibility: András Hajnal and Peter Hamburger ; translated by Attila Máté.
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'This is a classic introduction to set theory ...'. L'Enseignement Mathematique 'Give this book fifteen minutes attention - you will find that you must buy it! European Maths Society Journal

 
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