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Set Theory

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November 2004

Beschreibung

Beschreibung

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

Inhaltsverzeichnis

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.

Pressestimmen

'This is a classic introduction to set theory ...'. L'Enseignement Mathematique 'Give this book fifteen minutes attention - you will find that you must buy it! European Maths Society Journal
EAN: 9780521596671
ISBN: 052159667X
Untertitel: 'London Mathematical Society St'. English. Sprache: Englisch.
Verlag: CAMBRIDGE UNIV PR
Erscheinungsdatum: November 2004
Seitenanzahl: 324 Seiten
Übersetzer/Sprecher: Übersetzt von Attila Mate
Format: kartoniert
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