# 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
10.1 The Class $\mathbf {ON}$