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More About This Textbook
Overview
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.
Editorial Reviews
From the Publisher
"The great number of exercises and problems (some of them with hints for solution) makes this book a valuable text for mathematics majors and also for an undergraduate course in mathematical logic." Monatshefte fur MathematikProduct Details
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Table of Contents
Part I. Introduction to Set Theory: 1. Notation, conventions; 2. Definition of equivalence. The concept of cardinality. The axiom of choice; 3. Countable cardinal, continuum cardinal; 4. Comparison of cardinals; 5. Operations with sets and cardinals; 6. Examples; 7. Ordered sets. Order types. Ordinals; 8. Properties of well-ordered sets. Good sets. The ordinal operation; 9. Transfinite induction and recursion; 10. Definition of the cardinality operation. Properties of cardinalities. The confinality operation; 11. Properties of the power operation; Appendix. An axiomatic development of set theory; Part II. Topics in Combinatorial Set Theory: 12. Stationary sets; 13. Δ-systems; 14. Ramsey's theorem and its generalizations. Partition calculus; 15. Inaccessible cardinals. Mahlo cardinals; 16. Measurable cardinals; 17. Real-valued measurable cardinals, saturated ideas; 18. Weakly compact and Ramsey cardinals; 19. Set mappings; 20. The square-bracket symbol. Strengthenings of the Ramsey counterexamples; 21. Properties of the power operation; 22. Powers of singular cardinals. Shelah's theorem.