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

From ProofWiki
Jump to navigation Jump to search

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