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. The first part introduces all the standard notions of the subject; the second part concentrates on combinatorial set theory. Exercises are included throughout and a new section of hints has been added to assist the reader.
Author(s): Andras Hajnal, Peter Hamburger, Attila Mate
Series: London Mathematical Society Student Texts
Edition: 1st English
Publisher: Cambridge University Press
Year: 1999
Language: English
Pages: 324
Front Cover......Page cover.djvu
Front Matter......Page 0005.djvu
Preface......Page 0009.djvu
Part I. Introduction to set theory......Page 005.djvu
Introduction ......Page 0002.djvu
1. Notation, conventions......Page 0007.djvu
2. Definition of equivalence. The concept of cardinality. Axiom of Choice......Page 011.djvu
3. Countable cardinal, continuum cardinal......Page 015.djvu
4. Comparison of cardinals......Page 021.djvu
5. Operations with sets and cardinals......Page 028.djvu
6. Examples......Page 036.djvu
7. Ordered sets. Order types. Ordinals......Page 041.djvu
8. Properties of wellordered sets. Good sets. The ordinal operation ......Page 054.djvu
9. Transfinite induction and recursion. Some consequences of the Axiom of Choice, the Wellordering Theorem ......Page 066.djvu
10. Definition of the cardinality operation. Properties of cardinalities. The cofinality operation ......Page 077.djvu
11. Properties of the power operation......Page 093.djvu
Hints for solving problems marked with * in Part I......Page 101.djvu
Appendix. An axiomatic development of set theory......Page 106.djvu
Introduction......Page 109.djvu
AI. The Zermelo-Fraenkel axiom system of set theory......Page 111.djvu
A2. Definition of concepts; extension of the language......Page 114.djvu
A3. A sketch of the development. Metatheorems......Page 117.djvu
A4. A sketch of the development. Definitions of simple operations and properties (continued) ......Page 122.djvu
A5. A sketch of the development. Basic theorems, the introduction of omega and R (continued) ......Page 124.djvu
A6. The ZFC axiom system. A weakening of the Axiom of Choice. Remarks on the theorems of Sections 2-7 ......Page 128.djvu
A7. The role of the Axiom of Regularity ......Page 130.djvu
A8. Proofs of relative consistency. The method of interpretation......Page 133.djvu
A9. Proofs of relative consistency. The method of models......Page 138.djvu
Part II. Topics in combinatorial set theory......Page 143.djvu
12. Stationary sets ......Page 145.djvu
13. Delta-systems......Page 159.djvu
14. Ramsey's Theorem and its generalizations. Partition calculus......Page 164.djvu
15. Inaccessible cardinals. Mahlo cardinals......Page 184.djvu
16. Measurable cardinals......Page 190.djvu
17. Real-valued measurable cardinals, saturated ideals......Page 203.djvu
18. Weakly compact and Ramsey cardinals......Page 216.djvu
19. Set mappings......Page 228.djvu
20. The square-bracket symbol. Strengthenings of the Ramsey counterexamples......Page 234.djvu
21. Properties of the power operation. Results on the singular cardinal problem......Page 243.djvu
22. Powers of singular cardinals. Shelah's Theorem......Page 259.djvu
Hints for solving problems of Part II......Page 272.djvu
Bibliography......Page 295.djvu
List of symbols......Page 297.djvu
Name index......Page 301.djvu
Subject index......Page 303.djvu
Back Cover......Page cover_back.djvu
