The Joy of Sets

Fundamentals of Contemporary Set Theory

Devlin, Keith

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The Joy of Sets

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ISBN: 9780387940946, 208 blz., March 2019, Engels UITVERKOCHT!

Uitgever: Athenaeum Uitgeverij

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Preface v




Naive Set Theory

1(28)




What is a Set?

1(3)




Operations on Sets

4(2)




Notation for Sets

6(1)




Sets of Sets

7(3)




Relations

10(2)




Functions

12(4)




Well-Orderings and Ordinals

16(9)




Problems

25(4)




The Zermelo-Fraenkel Axioms

29(37)




The Language of Set Theory

30(5)




The Cumulative Hierarchy of Sets

35(5)




The Zermelo-Fraenkel Axioms

40(6)




Classes

46(4)




Set Theory as an Axiomatic Theory

50(1)




The Recursion Principle

51(5)




The Axiom of Choice

56(7)




Problems

63(3)




Ordinal and Cardinal Numbers

66(35)




Ordinal Numbers

66(2)




Addition of Ordinals

68(1)




Multiplication of Ordinals

69(2)




Sequences of Ordinals

71(3)




Ordinal Exponentiation

74(1)




Cardinality, Cardinal Numbers

75(7)




Arithmetic of Cardinal Numbers

82(6)




Regular and Singular Cardinals

88(3)




Cardinal Exponentiation

91(4)




Inaccessible Cardinals

95(3)




Problems

98(3)




Topics in Pure Set Theory

101(19)




The Borel Hierarchy

101(2)




Closed Unbounded Sets

103(3)




Stationary Sets and Regressive Functions

106(3)




Trees

109(4)




Extensions of Lebesgue Measure

113(3)




A Result About the GCH

116(4)




The Axiom of Constructibility

120(10)




Constructible Sets

120(3)




The Constructible Hierarchy

123(1)




The Axiom of Constructibility

124(3)




The Consistency of V = L

127(1)




Use of the Axiom of Constructibility

128(2)




Independence Proofs in Set Theory

130(13)




Some Undecidable Statements

130(1)




The Idea of a Boolean-Valued Universe

130(3)




The Boolean-Valued Universe

133(3)




VB and V

136(1)




Boolean-Valued Sets and Independence Proofs

137(2)




The Nonprovability of the CH

139(4)




Non-Well-Founded Set Theory

143(42)




Set-Membership Diagrams

145(6)




The Anti-Foundation Axiom

151(5)




The Solution Lemma

156(3)




Inductive Definitions Under AFA

159(4)




Graphs and Systems

163(5)




Proof of the Solution Lemma

168(1)




Co-Inductive Definitions

169(4)




A Model of ZF- +AFA

173(12)
Bibliography 185(1)
Glossary of Symbols 185(4)
Index 189
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