Set theory

Description

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