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

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