Classic Set Theory : For Guided Independent Study (Paperback)

INTRODUCTION
Outline of the book
Assumed knowledge

THE REAL NUMBERS
Introduction
Dedekind's construction
Alternative constructions
The rational numbers

THE NATURAL NUMBERS
Introduction
The construction of the natural numbers
Arithmetic
Finite sets

THE ZERMELO-FRAENKEL AXIOMS
Introduction
A formal language
Axioms 1 to 3
Axioms 4 to 6
Axioms 7 to 9

CARDINAL (Without the Axiom of Choice)
Introduction
Comparing Sizes
Basic properties of ? and =
Infinite sets without AC-countable sets
Uncountable sets and cardinal arithmetic without AC

ORDERED SETS
Introduction
Linearly ordered sets
Order arithmetic
Well-ordered sets

ORDINAL NUMBERS
Introduction
Ordinal numbers
Beginning ordinal arithmetic
Ordinal arithmetic
The As

SET THEORY WITH THE AXIOM OF CHOICE
Introduction
The well-ordering principle
Cardinal arithmetic and the axiom of choice
The continuum hypothesis

BIBLIOGRAPHY
INDEX