# Book:Winfried Just/Discovering Modern Set Theory. I: The Basics

## Winfried Just and Martin Weese: Discovering Modern Set Theory. I: The Basics

Published $\text {1996}$, American Mathematical Society

ISBN 0-8218-0266-6.

### Contents

Preface
Basic Notations
Introduction
Part $1$. Not Entirely Naive Set Theory
Chapter $1$. Pairs, Relations, and Functions
Chapter $2$. Partial Order Relations
Chapter $3$. Cardinality
Chapter $4$. Induction
$4.1$ Induction and recursion over the set of natural numbers
$4.2$ Induction and recursion over wellfounded sets
Part $2$. An Axiomatic Foundation of Set Theory
Chapter $5$. Formal Languages and Models
Chapter $6$. Power and Limitations of the Axiomatic Method
$6.1$ Complete theories
$6.2$ The Incompleteness Phenomenon
$6.3$ Definability
Chapter $7$. The Axioms
Chapter $8$. Classes
Chapter $9$. Versions of the Axiom of Choice
$9.1$ Statements Equivalent to the Axiom of Choice
$9.2$ Set Theory without the Axiom of Choice
$9.3$ The Axiom of Determinacy
$9.4$ The Banach-Tarski Paradox
Chapter $10$. The Ordinals
$10.1$ The Class $\mathbf {ON}$
$10.2$ Ordinal Arithmetic
Chapter $11$. The Cardinals
$11.1$ Initial Ordinals
$11.2$ Cardinal Arithmetic
Chapter $12$. Pictures of the Universe
Subject index
Index of notation

Next

## Source work progress

A complexity raised here which needs to be resolved: