Elements of Set Theory

<br>Contents</br><br>Preface </br><br>List of Symbols </br><br>Chapter 1 Introduction </br><br> Baby Set Theory </br><br> Sets—An Informal View</br><br> Classes</br><br> Axiomatic Method </br><br> Notation </br><br> Historical Notes </br><br>Chapter 2 Axioms and Operations</br><br> Axioms </br><br> Arbitrary Unions and Intersections </br><br> Algebra of Sets </br><br> Epilogue </br><br> Review Exercises </br><br>Chapter 3 Relations and Functions</br><br> Ordered Pairs</br><br> Relations </br><br> n-Ary Relations </br><br> Functions </br><br> Infinite Cartesian Products</br><br> Equivalence Relations </br><br> Ordering Relations </br><br> Review Exercises </br><br>Chapter 4 Natural Numbers </br><br> Inductive Sets </br><br> Peano's Postulates </br><br> Recursion on ω </br><br> Arithmetic </br><br> Ordering on ω</br><br> Review Exercises </br><br>Chapter 5 Construction of the Real Numbers</br><br> Integers </br><br> Rational Numbers </br><br> Real Numbers </br><br> Summaries </br><br> Two </br><br>Chapter 6 Cardinal Numbers and the Axiom of Choice</br><br> Equinumerosity </br><br> Finite Sets </br><br> Cardinal Arithmetic </br><br> Ordering Cardinal Numbers </br><br> Axiom of Choice </br><br> Countable Sets </br><br> Arithmetic of Infinite Cardinals </br><br> Continuum Hypothesis </br><br>Chapter 7 Orderings and Ordinals</br><br> Partial Orderings </br><br> Well Orderings </br><br> Replacement Axioms </br><br> Epsilon-Images </br><br> Isomorphisms </br><br> Ordinal Numbers </br><br> Debts Paid </br><br> Rank </br><br>Chapter 8 Ordinals and Order Types</br><br> Transfinite Recursion Again </br><br> Alephs </br><br> Ordinal Operations </br><br> Isomorphism Types </br><br> Arithmetic of Order Types </br><br> Ordinal Arithmetic </br><br>Chapter 9 Special Topics</br><br> Well-Founded Relations</br><br> Natural Models </br><br> Cofinality </br><br>Appendix Notation, Logic, and Proofs </br><br>Selected References for Further Study</br><br>List of Axioms</br><br>Index</br><br></br><br></br>