Set theory / András Hajnal, Peter Hamburger ; translated by Attila Máté.

Format:

Book

Author/Creator:

Hajnal, A.

Contributor:

Hamburg, P.

Series:

London Mathematical Society student texts ; 48.

London Mathematical Society student texts ; 48

Standardized Title:

Halmazeimelét

Language:

English

Hungarian

Subjects (All):

Set theory.

Physical Description:

viii, 316 pages ; 24 cm.

Place of Publication:

Cambridge, U.K. ; New York : Cambridge University Press, 1999.

Summary:

This is a classic introduction to set theory, suitable for students with no previous knowledge of the subject. Providing complete, up-to-date coverage, the book is based in large part on courses given over many years by Professor Hajnal.

Contents:

2. Definition of equivalence. The concept of cardinality. The Axiom of Choice 11

3. Countable cardinal, continuum cardinal 15

4. Comparison of cardinals 21

5. Operations with sets and cardinals 28

7. Ordered sets. Order types. Ordinals 41

8. Properties of wellordered sets. Good sets. The ordinal operation 54

9. Transfinite induction and recursion. Some consequences of the Axiom of Choice, the Wellordering Theorem 66

10. Definition of the cardinality operation. Properties of cardinalities. The cofinality operation 77

11. Properties of the power operation 93

Hints for solving problems marked with * in Part I 101

Appendix An axiomatic development of set theory 107

A1. The Zermelo-Fraenkel axiom system of set theory 111

A2. Definition of concepts; extension of the language 114

A3. A sketch of the development. Metatheorems 117

A4. A sketch of the development. Definitions of simple operations and properties (continued) 122

A5. A sketch of the development. Basic theorems, the introduction of [omega] and R (continued) 124

A6. The ZFC axiom system. A weakening of the Axiom of Choice. Remarks on the theorems of Sections 2-7 128

A7. The role of the Axiom of Regularity 130

A8. Proofs of relative consistency. The method of interpretation 133

A9. Proofs of relative consistency. The method of models 138

Part II. Topics in combinatorial set theory 143

12. Stationary sets 145

13. [Delta]-systems 159

14. Ramsey's Theorem and its generalizations. Partition calculus 164

15. Inaccessible cardinals. Mahlo cardinals 184

16. Measurable cardinals 190

17. Real-valued measurable cardinals, saturated ideals 203

18. Weakly compact and Ramsey cardinals 216

19. Set mappings 228

20. The square-bracket symbol. Strengthenings of the Ramsey counterexamples 234

21. Properties of the power operation. Results on the singular cardinal problem 243

22. Powers of singular cardinals. Shelah's Theorem 259.

Notes:

Includes bibliographical references (pages [295]-296) and indexes.

ISBN:

0521593441

052159667X

OCLC:

41143004