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
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
