Set Theory

Set Theory

by Andras Hajnal, Peter Hamburger

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


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

Product Details

Cambridge University Press
Publication date:
London Mathematical Society Student Texts Series, #48
Product dimensions:
5.98(w) x 8.98(h) x 0.87(d)

Table of Contents

Pt. IIntroduction to set theory1
1Notation, conventions5
2Definition of equivalence. The concept of cardinality. The Axiom of Choice11
3Countable cardinal, continuum cardinal15
4Comparison of cardinals21
5Operations with sets and cardinals28
7Ordered sets. Order types. Ordinals41
8Properties of wellordered sets. Good sets. The ordinal operation54
9Transfinite induction and recursion. Some consequences of the Axiom of Choice, the Wellordering Theorem66
10Definition of the cardinality operation. Properties of cardinalities. The cofinality operation77
11Properties of the power operation93
AppAn axiomatic development of set theory107
A1The Zermelo-Fraenkel axiom system of set theory111
A2Definition of concepts; extension of the language114
A3A sketch of the development. Metatheorems117
A4A sketch of the development. Definitions of simple operations and properties (continued)122
A5A sketch of the development. Basic theorems, the introduction of [omega] and R (continued)124
A6The ZFC axiom system. A weakening of the Axiom of Choice. Remarks on the theorems of Sections 2-7128
A7The role of the Axiom of Regularity130
A8Proofs of relative consistency. The method of interpretation133
A9Proofs of relative consistency. The method of models138
Pt. IITopics in combinatorial set theory143
12Stationary sets145
14Ramsey's Theorem and its generalizations. Partition calculus164
15Inaccessible cardinals. Mahlo cardinals184
16Measurable cardinals190
17Real-valued measurable cardinals, saturated ideals203
18Weakly compact and Ramsey cardinals216
19Set mappings228
20The square-bracket symbol. Strengthenings of the Ramsey counterexamples234
21Properties of the power operation. Results on the singular cardinal problem243
22Powers of singular cardinals. Shelah's Theorem259
List of symbols297
Name index301
Subject index303

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