{"product_id":"set-theory-paperback-9780521596671","title":"Set Theory (Paperback) 9780521596671","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eSet Theory\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eThis is a classic introduction to set theory, from the basics through to the modern tools of combinatorial set theory.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eAndras Hajnal (Author), Peter Hamburger (Author), Attila Mate (Translated by)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521596671, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback, published 11 November 1999\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e328 pages\u003cbr\u003e22.9 x 15.2 x 1.9 cm, 0.48 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e'Give this book fifteen minutes attention - you will find that you must buy it! European Maths Society Journal\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis is a classic introduction to set theory in three parts. The first part gives a general introduction to set theory, suitable for undergraduates; complete proofs are given and no background in logic is required. Exercises are included, and the more difficult ones are supplied with hints. An appendix to the first part gives a more formal foundation to axiomatic set theory, supplementing the intuitive introduction given in the first part. The final part gives an introduction to modern tools of combinatorial set theory. This part contains enough material for a graduate course of one or two semesters. The subjects discussed include stationary sets, delta systems, partition relations, set mappings, measurable and real-valued measurable cardinals. Two sections give an introduction to modern results on exponentiation of singular cardinals, and certain deeper aspects of the topics are developed in advanced problems.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePart I. Introduction to Set Theory: 1. Notation, conventions\u003cbr\u003e 2. Definition of equivalence. The concept of cardinality. The axiom of choice\u003cbr\u003e 3. Countable cardinal, continuum cardinal\u003cbr\u003e 4. Comparison of cardinals\u003cbr\u003e 5. Operations with sets and cardinals\u003cbr\u003e 6. Examples\u003cbr\u003e 7. Ordered sets. Order types. Ordinals\u003cbr\u003e 8. Properties of well-ordered sets. Good sets. The ordinal operation\u003cbr\u003e 9. Transfinite induction and recursion\u003cbr\u003e 10. Definition of the cardinality operation. Properties of cardinalities. The confinality operation\u003cbr\u003e 11. Properties of the power operation\u003cbr\u003e Appendix. An axiomatic development of set theory\u003cbr\u003e Part II. Topics in Combinatorial Set Theory: 12. Stationary sets\u003cbr\u003e 13. Delta-systems\u003cbr\u003e 14. Ramsey's theorem and its generalizations. Partition calculus\u003cbr\u003e 15. Inaccessible cardinals. Mahlo cardinals\u003cbr\u003e 16. Measurable cardinals\u003cbr\u003e 17. Real-valued measurable cardinals, saturated ideas\u003cbr\u003e 18. Weakly compact and Ramsey cardinals\u003cbr\u003e 19. Set mappings\u003cbr\u003e 20. The square-bracket symbol. Strengthenings of the Ramsey counterexamples\u003cbr\u003e 21. Properties of the power operation\u003cbr\u003e 22. Powers of singular cardinals. Shelah's theorem.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Set theory [\u003ca title=\"See our other books on Set theory\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Set%20theory%20%5BPBCH%5D%22\"\u003ePBCH\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46004719485208,"sku":"9780521596671","price":56.19,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521596671i_d44f200c-234c-471b-a6f1-8d0b86adc933.jpg?v=1691370207","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/set-theory-paperback-9780521596671","provider":"Freshly Printed Books","version":"1.0","type":"link"}