Andras Hajnal, Peter Hamburger

Set Theory

• Broschiertes Buch

Produktbeschreibung

This is a classic introduction to set theory, from the basics through to the modern tools of combinatorial set theory.

Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 328
• Erscheinungstermin: 17. November 2004
• Englisch
• Abmessung: 229mm x 152mm x 19mm
• Gewicht: 534g
• ISBN-13: 9780521596671
• ISBN-10: 052159667X
• Artikelnr.: 21286791

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.