{"title":"Set theory","description":"Books on the subject of Set theory","products":[{"product_id":"elements-of-set-theory-hardback-9780122384400","title":"Elements of Set Theory (Hardback) 9780122384400","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eElements of Set Theory\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eHerbert B. Enderton (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780122384400, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 23 May 1977\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e296 pages\u003cbr\u003e22.9 x 15.1 x 2.3 cm, 0.53 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eContents\u003cbr\u003ePreface \u003cbr\u003eList of Symbols \u003cbr\u003eChapter 1 Introduction \u003cbr\u003e     Baby Set Theory \u003cbr\u003e     Sets—An Informal View\u003cbr\u003e     Classes\u003cbr\u003e     Axiomatic Method \u003cbr\u003e     Notation \u003cbr\u003e     Historical Notes \u003cbr\u003eChapter 2 Axioms and Operations\u003cbr\u003e     Axioms \u003cbr\u003e     Arbitrary Unions and Intersections \u003cbr\u003e     Algebra of Sets \u003cbr\u003e     Epilogue \u003cbr\u003e     Review Exercises \u003cbr\u003eChapter 3 Relations and Functions\u003cbr\u003e     Ordered Pairs\u003cbr\u003e     Relations \u003cbr\u003e     n-Ary Relations \u003cbr\u003e     Functions \u003cbr\u003e     Infinite Cartesian Products\u003cbr\u003e     Equivalence Relations \u003cbr\u003e     Ordering Relations \u003cbr\u003e     Review Exercises \u003cbr\u003eChapter 4 Natural Numbers \u003cbr\u003e     Inductive Sets \u003cbr\u003e     Peano's Postulates \u003cbr\u003e     Recursion on ? \u003cbr\u003e     Arithmetic \u003cbr\u003e     Ordering on ?\u003cbr\u003e     Review Exercises \u003cbr\u003eChapter 5 Construction of the Real Numbers\u003cbr\u003e     Integers \u003cbr\u003e     Rational Numbers \u003cbr\u003e     Real Numbers \u003cbr\u003e     Summaries \u003cbr\u003e     Two \u003cbr\u003eChapter 6 Cardinal Numbers and the Axiom of Choice\u003cbr\u003e     Equinumerosity \u003cbr\u003e     Finite Sets \u003cbr\u003e     Cardinal Arithmetic \u003cbr\u003e     Ordering Cardinal Numbers \u003cbr\u003e     Axiom of Choice \u003cbr\u003e     Countable Sets \u003cbr\u003e     Arithmetic of Infinite Cardinals \u003cbr\u003e     Continuum Hypothesis \u003cbr\u003eChapter 7 Orderings and Ordinals\u003cbr\u003e     Partial Orderings \u003cbr\u003e     Well Orderings \u003cbr\u003e     Replacement Axioms \u003cbr\u003e     Epsilon-Images \u003cbr\u003e     Isomorphisms \u003cbr\u003e     Ordinal Numbers \u003cbr\u003e     Debts Paid \u003cbr\u003e     Rank \u003cbr\u003eChapter 8 Ordinals and Order Types\u003cbr\u003e     Transfinite Recursion Again \u003cbr\u003e     Alephs \u003cbr\u003e     Ordinal Operations \u003cbr\u003e     Isomorphism Types \u003cbr\u003e     Arithmetic of Order Types \u003cbr\u003e     Ordinal Arithmetic \u003cbr\u003eChapter 9 Special Topics\u003cbr\u003e     Well-Founded Relations\u003cbr\u003e     Natural Models \u003cbr\u003e     Cofinality \u003cbr\u003eAppendix Notation, Logic, and Proofs \u003cbr\u003eSelected References for Further Study\u003cbr\u003eList of Axioms\u003cbr\u003eIndex\u003cbr\u003e\u003cbr\u003e\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], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Academic Press","offers":[{"title":"Default Title","offer_id":46648082825496,"sku":"9780122384400","price":46.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780122384400_f4afb8fe-e455-42ca-ade4-851acce2bbda.jpg?v=1695006725"},{"product_id":"set-theory-an-introduction-to-independence-proofs-hardback-9780444868398","title":"Set Theory An Introduction To Independence Proofs (Hardback) 9780444868398","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eSet Theory An Introduction To Independence Proofs\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eK. Kunen (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780444868398, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 1 December 1983\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e330 pages\u003cbr\u003e22.5 x 14.9 x 2.4 cm, 0.53 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eStudies in Logic and the Foundations of Mathematics, Volume 102: Set Theory: An Introduction to Independence Proofs offers an introduction to relative consistency proofs in axiomatic set theory, including combinatorics, sets, trees, and forcing.  The book first tackles the foundations of set theory and infinitary combinatorics. Discussions focus on the Suslin problem, Martin's axiom, almost disjoint and quasi-disjoint sets, trees, extensionality and comprehension, relations, functions, and well-ordering, ordinals, cardinals, and real numbers. The manuscript then ponders on well-founded sets and easy consistency proofs, including relativization, absoluteness, reflection theorems, properties of well-founded sets, and induction and recursion on well-founded relations. The publication examines constructible sets, forcing, and iterated forcing. Topics include Easton forcing, general iterated forcing, Cohen model, forcing with partial functions of larger cardinality, forcing with finite partial functions, and general extensions.   The manuscript is a dependable source of information for mathematicians and researchers interested in set theory.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eThe Foundations of Set Theory. Infinitary Combinatorics. The Well-Founded Sets. Easy Consistency Proofs. Defining Definability. The Constructible Sets. Forcing. Iterated Forcing. Bibliography. Indexes.\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":"North Holland","offers":[{"title":"Default Title","offer_id":46648514150680,"sku":"9780444868398","price":38.89,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780444868398_da78858c-39dd-4dd1-b9a9-3ab90522504d.jpg?v=1694987460"},{"product_id":"sets-and-extensions-in-the-twentieth-century-hardback-9780444516213","title":"Sets and Extensions in the Twentieth Century (Hardback) 9780444516213","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eSets and Extensions in the Twentieth Century\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eCovers the rich history of scientific turning points in set theory, providing fresh insights and points of view\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eDov M. Gabbay (Volume editor), Akihiro Kanamori (Volume editor), John Woods (Volume editor)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780444516213, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 24 January 2012\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e880 pages\u003cbr\u003e25.7 x 18.2 x 4.3 cm, 1.97 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eSet theory is an autonomous and sophisticated field of mathematics that is extremely successful at analyzing mathematical propositions and gauging their consistency strength. It is as a field of mathematics that both proceeds with its own internal questions and is capable of contextualizing over a broad range, which makes set theory an intriguing and highly distinctive subject. This handbook covers the rich history of scientific turning points in set theory, providing fresh insights and points of view. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in mathematics, the history of philosophy, and any discipline such as computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eSet Theory from Cantor to Cohen, by Akihiro Kanamori History of the Continuum in the 20th Century, by Juris Stepr¯ans Infinite Combinatorics, by Jean A. Larson Large Cardinals with Forcing, by Akihiro Kanamori Inner Models for Large Cardinals, by William J. Mitchell A Brief History of Determinacy, by Paul B. Larson Singular Cardinals: From Hausdorff’s Gaps to Shelah’s pcf Theory, by Menachem Kojman Alternative Set Theories, by M. Randall Holmes, Thomas Forster, and Thierry Libert Types, Sets, and Categories, by John L. Bell The History of Categorical Logic: 1963–1977, by Jean-Pierre Marquis and Gonzalo E. Reyes Russell’s Orders in Kripke’s Theory of Truth and Computational Type Theory, by Fairouz Kamareddine, Twan Laan, and Robert Constable\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: History of mathematics [\u003ca title=\"See our other books on History of mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22History%20of%20mathematics%20%5BPBX%5D%22\"\u003ePBX\u003c\/a\u003e], 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], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e], Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e], Philosophy: logic [\u003ca title=\"See our other books on Philosophy: logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Philosophy:%20logic%20%5BHPL%5D%22\"\u003eHPL\u003c\/a\u003e], Computational linguistics [\u003ca title=\"See our other books on Computational linguistics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Computational%20linguistics%20%5BCFX%5D%22\"\u003eCFX\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"North Holland","offers":[{"title":"Default Title","offer_id":46649075597592,"sku":"9780444516213","price":173.25,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780444516213.jpg?v=1694979961"},{"product_id":"theory-of-relations-hardback-9780444505422","title":"Theory of Relations (Hardback) 9780444505422","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eTheory of Relations\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eR. Fraisse (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780444505422, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 15 December 2000\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e456 pages\u003cbr\u003e22.9 x 15.1 x 2.8 cm, 0.78 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eRelation theory originates with Hausdorff (Mengenlehre 1914) and Sierpinski (Nombres transfinis, 1928) with the study of order types, specially among chains = total orders = linear orders.  One of its first important problems was partially solved by Dushnik, Miller 1940 who, starting from the chain of reals, obtained an infinite strictly decreasing sequence of chains (of continuum power) with respect to embeddability.  In 1948 I conjectured that every strictly decreasing sequence of denumerable chains is finite.  This was affirmatively proved by Laver (1968), in the more general case of denumerable unions of scattered chains (ie: which do not embed the chain Q of rationals), by using the barrier and the better orderin gof Nash-Williams (1965 to 68). \u003cbr\u003eAnother important problem is the extension to posets of classical properties of chains.  For instance one easily sees that a chain A is scattered if the chain of inclusion of its initial intervals is itself scattered (6.1.4).  Let us again define a scattered poset A by the non-embedding of Q in A.  We say that A is finitely free if every antichain restriction of A is finite (antichain = set of mutually incomparable elements of the base). In 1969 Bonnet and Pouzet proved that a poset A is finitely free and scattered iff the ordering of inclusion of initial intervals of A is scattered.  In 1981 Pouzet proved the equivalence with the a priori stronger condition that A is topologically scattered: (see 6.7.4; a more general result is due to Mislove 1984); ie: every non-empty set of initial intervals contains an isolated elements for the simple convergence topology. \u003cbr\u003eIn chapter 9 we begin the general theory of relations, with the notions of local isomorphism, free interpretability and free operator (9.1 to 9.3), which is the relationist version of a free logical formula.  This is generalized by the back-and-forth notions in 10.10: the (k,p)-operator is the relationist version of the elementary formula (first order formula with equality). \u003cbr\u003eChapter 12 connects relation theory with permutations: theorem of the increasing number of orbits (Livingstone, Wagner in 12.4). Also in this chapter homogeneity is introduced, then more deeply studied in the Appendix written by Norbert Saucer. \u003cbr\u003eChapter 13 connects relation theory with finite permutation groups;  the main notions and results are due to Frasnay.  Also mention the extension to relations of adjacent elements, by Hodges, Lachlan, Shelah who by this mean give an exact calculus of the reduction threshold. \u003cbr\u003eThe book covers almost all present knowledge in Relation Theory, from origins (Hausdorff 1914, Sierpinski 1928) to classical results (Frasnay 1965, Laver 1968, Pouzet 1981) until recent important publications (Abraham, Bonnet 1999). \u003cbr\u003eAll results are exposed in axiomatic set theory.  This allows us, for each statement, to specify if it is proved only from ZF axioms of choice, the continuum hypothesis or only the ultrafilter axiom or the axiom of dependent choice, for instance.\u003cbr\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eIntroduction. 1. Review of axiomatic set theory, relation. 2. Coherence lemma, cofinality, tree, ideal. 3. Ramsey theorem, partition, incidence matrix. 4. Good, bad sequence, well partial ordering. 5. Embeddability between relations and chains. 6. Scattered chain, scattered poset. 7. Well quasi-ordering of scattered chains. 8. Bivalent tableau, Szpilrajn chain. 9. Free operator, chainability, strong interval. 10. Age, \u0026amp;agr\u003cbr\u003e-morphism, back-and-forth. 11. Relative isomorphism, saturated relation. 12. Homogeneous relation, orbit. 13. Compatibility and chainability theorems. A. On countable homogeneous systems: Sauer\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], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"North Holland","offers":[{"title":"Default Title","offer_id":46651423621400,"sku":"9780444505422","price":129.65,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780444505422.jpg?v=1694979892"}],"url":"https:\/\/freshlyprintedbooks.co.uk\/collections\/set-theory.oembed","provider":"Freshly Printed Books","version":"1.0","type":"link"}