LEADER 04903nam 22005895 450 001 9910789344403321 005 20220321151032.0 010 $a1-4612-0903-X 024 7 $a10.1007/978-1-4612-0903-4 035 $a(CKB)3400000000089314 035 $a(SSID)ssj0001297324 035 $a(PQKBManifestationID)11775251 035 $a(PQKBTitleCode)TC0001297324 035 $a(PQKBWorkID)11362351 035 $a(PQKB)10433318 035 $a(DE-He213)978-1-4612-0903-4 035 $a(MiAaPQ)EBC3073428 035 $a(PPN)238033465 035 $a(EXLCZ)993400000000089314 100 $a20121227d1993 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 14$aThe Joy of Sets$b[electronic resource] $eFundamentals of Contemporary Set Theory /$fby Keith Devlin 205 $a2nd ed. 1993. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1993. 215 $a1 online resource (X, 194 p.) 225 1 $aUndergraduate Texts in Mathematics,$x0172-6056 300 $a"With 11 illustrations." 311 $a0-387-94094-4 311 $a1-4612-6941-5 320 $aIncludes bibliographical references and index. 327 $a1 Naive Set Theory -- 1.1 What is a Set? -- 1.2 Operations on Sets -- 1.3 Notation for Sets -- 1.4 Sets of Sets -- 1.5 Relations -- 1.6 Functions -- 1.7 Well-Or der ings and Ordinals -- 1.8 Problems -- 2 The Zermelo?Fraenkel Axioms -- 2.1 The Language of Set Theory -- 2.2 The Cumulative Hierarchy of Sets -- 2.3 The Zermelo?Fraenkel Axioms -- 2.4 Classes -- 2.5 Set Theory as an Axiomatic Theory -- 2.6 The Recursion Principle -- 2.7 The Axiom of Choice -- 2.8 Problems -- 3 Ordinal and Cardinal Numbers -- 3.1 Ordinal Numbers -- 3.2 Addition of Ordinals -- 3.3 Multiplication of Ordinals -- 3.4 Sequences of Ordinals -- 3.5 Ordinal Exponentiation -- 3.6 Cardinality, Cardinal Numbers -- 3.7 Arithmetic of Cardinal Numbers -- 3.8 Regular and Singular Cardinals -- 3.9 Cardinal Exponentiation -- 3.10 Inaccessible Cardinals -- 3.11 Problems -- 4 Topics in Pure Set Theory -- 4.1 The Borel Hierarchy -- 4.2 Closed Unbounded Sets -- 4.3 Stationary Sets and Regressive Functions -- 4.4 Trees -- 4.5 Extensions of Lebesgue Measure -- 4.6 A Result About the GCH -- 5 The Axiom of Constructibility -- 5.1 Constructible Sets -- 5.2 The Constructible Hierarchy -- 5.3 The Axiom of Constructibility -- 5.4 The Consistency of V = L -- 5.5 Use of the Axiom of Constructibility -- 6 Independence Proofs in Set Theory -- 6.1 Some Undecidable Statements -- 6.2 The Idea of a Boolean-Valued Universe -- 6.3 The Boolean-Valued Universe -- 6.4 VB and V -- 6.5 Boolean-Valued Sets and Independence Proofs -- 6.6 The Nonprovability of the CH -- 7 Non-Well-Founded Set Theory -- 7.1 Set-Membership Diagrams -- 7.2 The Anti-Foundation Axiom -- 7.3 The Solution Lemma -- 7.4 Inductive Definitions Under AFA -- 7.5 Graphs and Systems -- 7.6 Proof of the Solution Lemma -- 7.7 Co-Inductive Definitions -- 7.8 A Model of ZF- +AFA -- Glossary of Symbols. 330 $aThis book provides an account of those parts of contemporary set theory of direct relevance to other areas of pure mathematics. The intended reader is either an advanced-level mathematics undergraduate, a beginning graduate student in mathematics, or an accomplished mathematician who desires or needs some familiarity with modern set theory. The book is written in a fairly easy-going style, with minimal formalism. In Chapter 1, the basic principles of set theory are developed in a 'naive' manner. Here the notions of 'set', 'union', 'intersection', 'power set', 'rela­ tion', 'function', etc., are defined and discussed. One assumption in writing Chapter 1 has been that, whereas the reader may have met all of these 1 concepts before and be familiar with their usage, she may not have con­ sidered the various notions as forming part of the continuous development of a pure subject (namely, set theory). Consequently, the presentation is at the same time rigorous and fast. 410 0$aUndergraduate Texts in Mathematics,$x0172-6056 606 $aMathematical logic 606 $aComputer science$xMathematics 606 $aMathematical Logic and Foundations$3https://scigraph.springernature.com/ontologies/product-market-codes/M24005 606 $aMath Applications in Computer Science$3https://scigraph.springernature.com/ontologies/product-market-codes/I17044 615 0$aMathematical logic. 615 0$aComputer science$xMathematics. 615 14$aMathematical Logic and Foundations. 615 24$aMath Applications in Computer Science. 676 $a511.3 700 $aDevlin$b Keith J$4aut$4http://id.loc.gov/vocabulary/relators/aut$028052 701 $aDevlin$b Keith J$028052 906 $aBOOK 912 $a9910789344403321 996 $aThe Joy of Sets$93720393 997 $aUNINA