Introduction to Modern Set Theory

Some Mathematical Preliminaries.

Partially Ordered Sets.

Some Facts About Partially Ordered Sets.

Equivalence Relations.

Well-Ordered Sets.

Mathematical Induction.

Models.

THE AXIOMS, PART I. The Language, Some Finite Operations, and Extensionality.

Pairs.

Cartesian Products.

Union, Intersection, and Separation.

Filters and Ideas.

The Natural Numbers.

Two Nonconstructive Axioms: Infinity and Power Set.

A Digression on the Power Set Axiom.

Replacement.

REGULARITY AND CHOICE.

Transitive Sets.

A First Look at Ordinals.

Regularity.

A World About Classes.

The Axiom of Choice.

Four Forms of the Axiom of Choice.

Models of Regularity and Choice.

THE FOUNDATION OF MATHEMATICS.

INFINITE NUMBERS.

Cardinality.

Ordinal Arithmetic.

Cardinal Arithmetic.

Cofinality.

Infinite Operations and More Exponentiation.

Counting.

TWO MODELS OF SET THEORY.

A Set Model for ZFC.

The Constructible Universe.

INFINITE COMBINATORICS.

Partition Calculus.

Trees.

Measurable Cardinals.

CH.

Martin's Axiom.

Stationary Sets.

Bibliography.

Index.