Andras Hajnal, A. Hajnal, Peter Hamburgerm

Set Theory

• Gebundenes Buch

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 328
• Erscheinungstermin: 30. November 2009
• Englisch
• Abmessung: 235mm x 157mm x 24mm
• Gewicht: 685g
• ISBN-13: 9780521593441
• ISBN-10: 0521593441
• Artikelnr.: 22473767

Inhaltsangabe

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. Delta-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.