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

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

Published $1996$, American Mathematical Society

ISBN 0-8218-0266-6.

Subject Matter

• Set Theory

Contents

Preface

How to Read this Book

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