Elements of Set Theory, Enderton

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Contents
	Preface
	List of Symbols
	1. Introduction
	Baby set theory
	Sets - an informal view
	Classes
	Axiomatic method
	Notation
	Historical notes
	2. Axioms and Operations
	Axioms
	Arbitrary unions and intersections
	Algebra of sets
	Epilogue
	3. Relations and Functions
	Ordered pairs
	Relations
	n-ary relations
	Functions
	Infinite cartesian products
	Equivalence relations
	Ordering relations
	4. Natural Numbers
	Inductive sets
	Peano's postulates
	Recursion on ω
	Arithmetic
	Untitled
	Ordering on ω
	5. Construction of the Real Numbers
	Integers
	Rational numbers
	Real numbers
	Summaries
	Two
	6. Cardinal Numbers and the Axiom of Choice
	Equinumerosity
	Finite sets
	Cardinal arithmetic
	Ordering cardinal numbers
	Axiom of choice
	Countable sets
	Arithmetic of infinite cardinals
	Continuum hypothesis
	7. Orderings and Ordinals
	Partial orderings
	Well orderings
	Replacement axioms
	Epsilon-images
	Isomorphisms
	Ordinal numbers
	Debts paid
	Rank
	8. Ordinals and order types
	Transfinite recursion again
	Alephs
	Ordinal operations
	Isomorphism types
	Ordinal arithmetic
	9. Special Topics
	Well-founded relations
	Natural models
	Cofinality
	Appendix: Notation, Logic and Proofs
	Selected References for Further Study
	List of Axioms
	Index