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.
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.
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.
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.
Es gelten unsere Allgemeinen Geschäftsbedingungen: www.buecher.de/agb
Impressum
www.buecher.de ist ein Shop der buecher.de GmbH & Co. KG Bürgermeister-Wegele-Str. 12, 86167 Augsburg Amtsgericht Augsburg HRA 13309
