内容

目次

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. Ordertypes. Ordinals; 8. Properties of well-ordered sets. Good sets. The ordinaloperation; 9. Transfinite induction and recursion; 10. Definition of thecardinality operation. Properties of cardinalities. The confinalityoperation; 11. Properties of the power operation; Appendix. An axiomaticdevelopment of set theory; Part II. Topics in Combinatorial Set Theory: 12.Stationary sets; 13. Delta-systems; 14. Ramsey's theorem and itsgeneralizations. Partition calculus; 15. Inaccessible cardinals. Mahlocardinals; 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.