{"product_id":"a-book-of-set-theory","title":"A Book of Set Theory","description":"\n\u003ctable align=\"center\" border=\"0\" cellpadding=\"2\" cellspacing=\"0\" width=\"100%\"\u003e\n\u003ctr\u003e\n\u003ctd class=\"productDetailSmallElements\"\u003e\n\u003cp\u003e\n\u003cstrong\u003eMarc Notes\u003c\/strong\u003e:\u003cbr\u003e\n\t\t\t\t\t\t\t\tA revised and corrected republication of Set Theory, originally published in 1971 by Addison-Wesley Publishing Company, Reading, Massachusetts.;Includes bibliographical references and index.;This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author--;Provided by publisher.\u003cbr\u003e\u003cbr\u003e\n\u003cstrong\u003eTable of Contents\u003c\/strong\u003e:\u003cbr\u003e\n\t\t\t\t\t\t\t\tPreface -- Chapter 0. Historical Introduction -- 1. The background of set theory -- 2. The paradoxes -- 3. The axiomatic method -- 4. Axiomatic set theory -- 5. Objections to the axiomatic approach. Other proposals -- 6. Concluding remarks -- Chapter 1. Classes and Sets -- 1. Building sentences -- 2. Building classes -- 3. The algebra of classes -- 4. Ordered pairs Cartesian products -- 5. Graphs -- 6. Generalized union and intersection -- 7. Sets -- Chapter 2. Functions -- 1. Introduction -- 2. Fundamental concepts and definitions -- 3. Properties of composite functions and inverse functions -- 4. Direct images and inverse images under functions -- 5. Product of a family of classes -- 6. The axiom of replacement -- Chapter 3. Relations -- 1. Introduction -- 2. Fundamental concepts and definitions -- 3. Equivalence relations and partitions -- 4. Pre-image, restriction and quotient of equivalence relations -- 5. Equivalence relations and functions -- Chapter 4. Partially Ordered Classes -- 1. Fundamental concepts and definitions -- 2. Order preserving functions and isomorphism -- 3. Distinguished elements. Duality -- 4. Lattices -- 5. Fully ordered classes. Well-ordered classes -- 6. Isomorphism between well-ordered classes -- Chapter 5. The Axiom of Choice and Related Principles -- 1. Introduction -- 2. The axiom of choice -- 3. An application of the axiom of choice -- 4. Maximal principles -- 5. The well-ordering theorem -- 6. Conclusion -- Chapter 6. The Natural Numbers -- 1. Introduction -- 2. Elementary properties of the natural numbers -- 3. Finite recursion -- 4. Arithmetic of natural numbers -- 5. Concluding remarks -- Chapter 7. Finite and Infinite Sets -- 1. Introduction -- 2. Equipotence of sets -- 3. Properties of infinite sets -- 4. Properties of denumerable sets -- Chapter 8. Arithmetic of Cardinal Numbers -- 1. Introduction -- 2. Operations on cardinal numbers -- 3. Ordering of the cardinal numbers -- 4. Special properties of infinite cardinal numbers -- 5. Infinite sums and products of cardinal numbers -- Chapter 9. Arithmetic of the Ordinal Numbers -- 1. Introduction -- 2. Operations on ordinal numbers -- 3. Ordering of the ordinal numbers -- 4. The alephs and the continuum hypothesis -- 5. Construction of the ordinals and cardinals -- Chapter 10. Transfinite Recursion. Selected Topics in the Theory of Ordinals and Cardinals -- 1. Transfinite recursion -- 2. Properties of ordinal exponentiation -- 3. Normal form -- 4. Epsilon numbers -- 5. Inaccessible ordinals and cardinals -- Chapter 11. Consistency and Independence in Set Theory -- 1. What is a set? -- 2. Models -- 3. Independence results in set theory -- 4. The question of models of set theory -- 5. Properties of the constructible universe -- 6. The GOdel Theorems -- Bibliography -- Index.\u003cbr\u003e\u003cbr\u003e\n\u003cstrong\u003eJacket Description\/Back\u003c\/strong\u003e:\u003cbr\u003e\n\u003c\/p\u003e\n\u003cp\u003eSuitable for upper-level undergraduates, this accessible approach to set theory poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. Starting with a repetition of the familiar arguments of elementary set theory, the level of abstract thinking gradually rises for a progressive increase in complexity.\u003cbr\u003eA historical introduction presents a brief account of the growth of set theory, with special emphasis on problems that led to the development of the various systems of axiomatic set theory. Subsequent chapters explore classes and sets, functions, relations, partially ordered classes, and the axiom of choice. Other subjects include natural and cardinal numbers, finite and infinite sets, the arithmetic of ordinal numbers, transfinite recursion, and selected topics in the theory of ordinals and cardinals. This updated edition features new material by author Charles C. Pinter.\u003cbr\u003eDover (2014) revised and corrected republication of \u003ci\u003eSet Theory\u003c\/i\u003e, originally published by the Addison-Wesley Publishing Company, Reading, Massachusetts, 1971.\u003cbr\u003eSee every Dover book in print at\u003cbr\u003e\u003cb\u003ewww.doverpublications.com\u003c\/b\u003e\u003c\/p\u003e\n\u003cbr\u003e\u003cbr\u003e\n\u003cstrong\u003eBiographical Note\u003c\/strong\u003e:\u003cbr\u003e\n\t\t\t\t\t\t\t\tCharles Pinter is Professor Emeritus of Mathematics at Bucknell University and the author of Dover's highly successful \n\u003ci\u003eBook of Abstract Algebra.\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e\n\u003cstrong\u003eBrief Description\u003c\/strong\u003e:\u003cbr\u003e\n\t\t\t\t\t\t\t\t\"A revised and corrected republication of Set Theory, originally published in 1971 by Addison-Wesley Publishing Company, Reading, Massachusetts.\"\u003cbr\u003e\u003cbr\u003e\n\u003cstrong\u003ePublisher Marketing\u003c\/strong\u003e:\u003cbr\u003e\n\t\t\t\t\t\t\t\tSuitable for upper-level undergraduates, this accessible approach to set theory poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. Starting with a repetition of the familiar arguments of elementary set theory, the level of abstract thinking gradually rises for a progressive increase in complexity. \n\u003cbr\u003eA historical introduction presents a brief account of the growth of set theory, with special emphasis on problems that led to the development of the various systems of axiomatic set theory. Subsequent chapters explore classes and sets, functions, relations, partially ordered classes, and the axiom of choice. Other subjects include natural and cardinal numbers, finite and infinite sets, the arithmetic of ordinal numbers, transfinite recursion, and selected topics in the theory of ordinals and cardinals. This updated edition features new material by author Charles C. Pinter. \n\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\n\n\u003cbr\u003e\n\u003cbr\u003e\n\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\n","brand":"Dover Publications","offers":[{"title":"Default Title","offer_id":46431140118659,"sku":"SPTM-9780486497082","price":20.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0564\/6830\/8099\/files\/9780486497082_spiral.png?v=1769660059","url":"https:\/\/sebink.com\/products\/a-book-of-set-theory","provider":"Sebink","version":"1.0","type":"link"}