Set theory

Cover
Title page
Copyright page
Set Theory
	Contents
	1 Historical Roots
		1.1 Strings to Ordinals
		1.2 Quadrature to Cardinals
	2 The Notion of Set
		2.1 Collections
		2.2 Sets
	3 The Zermelo–Fraenkel Axioms
		3.1 Statement
		3.2 Motivation
	4 Immediate Consequences
		4.1 The Algebra of Sets
		4.2 The Algebra of Relations
		4.3 Functions, Orders, Equivalences
	5 Number Systems Within Set Theory
		5.1 Real to Complex
		5.2 Rational to Real
		5.3 Peano Postulates
	6 Infinities
		6.1 Cardinals
		6.2 Order Types
		6.3 Ordinals
		6.4 Alephs
	7 The Axiom of Choice
		7.1 Weak and Full Choice
		7.2 Equivalents of Choice
	8 Topics in Higher Set Theory
		8.1 Descriptive Set Theory
		8.2 Continuum Theory
		8.3 Combinatorial Set Theory
	9 Metamathematics of Set Theory
		9.1 Truth
		9.2 Inaccessible Cardinals and Their Status
		9.3 Inner Models and the Status of AC
		9.4 Forcing and the Status of CH
	10 Large Cardinals and Determinacy
		10.1 Beyond Inaccessibles
		10.2 Infinite Games
		10.3 Large Cardinals and Inner Models
	11 Concluding Philosophical Remarks
References
Acknowledgments