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



Source work progress
* : Part $1$: Not Entirely Naive Set Theory: Chapter $2$: Partial Order Relations: Exercise $15 \ \text {(b)}$


 * A complexity raised here which needs to be resolved:


 * : Part $1$: Not Entirely Naive Set Theory: Chapter $1$: Pairs, Relations, and Functions: Exercise $8$