Set theory /
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| Main Author: | |
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| Other Authors: | |
| Format: | Book |
| Language: | English Hungarian |
| Published: |
Cambridge ; New York :
Cambridge University Press,
1999.
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| Edition: | 1st English ed. |
| Series: | London Mathematical Society student texts ;
48. London Mathematical Society student texts ; 48 |
| Subjects: | |
| Online Access: | Table of contents Publisher description |
Table of Contents:
- Pt. 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 wellordered sets. Good sets. The ordinal operation. 9. Transfinite induction and recursion. Some consequences of the Axiom of Choice, the Wellordering Theorem. 10. Definition of the cardinality operation. Properties of cardinalities. The cofinality operation. 11. Properties of the power operation
- App. An axiomatic development of set theory. A1. The Zermelo-Fraenkel axiom system of set theory. A2. Definition of concepts; extension of the language. A3. A sketch of the development. Metatheorems. A4. A sketch of the development. Definitions of simple operations and properties (continued).
- A5. A sketch of the development. Basic theorems, the introduction of [omega] and R (continued). A6. The ZFC axiom system. A weakening of the Axiom of Choice. Remarks on the theorems of Sections 2-7. A7. The role of the Axiom of Regularity. A8. Proofs of relative consistency. The method of interpretation. A9. Proofs of relative consistency. The method of models
- Pt. 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 ideals. 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. Results on the singular cardinal problem. 22. Powers of singular cardinals. Shelah's Theorem.