Chapter 1 INTRODUCTION

Baby Set Theory

Sets—An Informal View

Classes

Axiomatic Method

Notation

Historical Notes

Chapter 2 AXIOMS AND OPERATIONS

Axioms

Arbitrary Unions and Intersections

Algebra of Sets

Epilogue

Review Exercises

Chapter 3 RELATIONS AND FUNCTIONS

Ordered Pairs

Relations

n-Ary Relations

Functions

Infinite Cartesian Products

Equivalence Relations

Ordering Relations

Review Exercises

Chapter 4 NATURAL NUMBERS

Inductive Sets

Peano’s Postulates

Recursion on ω

Arithmetic

Ordering on ω

Review Exercises

Chapter 5 CONSTRUCTION OF THE REAL NUMBERS

Integers

Rational Numbers

Real Numbers

Summaries

Two

Chapter 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

Chapter 7 ORDERINGS AND ORDINALS

Partial Orderings

Well Orderings

Replacement Axioms

Epsilon-Images

Isomorphisms

Ordinal Numbers

Debts Paid

Rank

Chapter 8 ORDINALS AND ORDER TYPES

Transfinite Recursion Again

Alephs

Ordinal Operations

Isomorphism Types

Arithmetic of Order Types

Ordinal Arithmetic

Chapter 9 SPECIAL TOPICS

Well-Founded Relations

Natural Models

Cofinality

Appendix NOTATION, LOGIC, AND PROOFS

Selected References for Further Study

List of Axioms

Index