Book:Paul Bernays/Axiomatic Set Theory

Subject Matter

 * Axiomatic Set Theory

Contents

 * Historical introduction by Abraham Fraenkel:
 * Introductory Remarks
 * Zermelo's System. Equality and Extensionality
 * "Constructive" Axioms of "General" Set Theory
 * The Axiom of Choice
 * Axioms of Infinity and Restriction
 * Development of Set-Theory from the Axioms of Z
 * Remarks on the Axiom Systems of von Neumann, Bernays, Gödel


 * Axiomatic Set Theory
 * The Frame of Logic and Class Theory
 * The Start of General Set Theory
 * Ordinals; Natural Numbers; Finite Sets
 * Transfinite Recursion
 * Power; Order; Wellorder
 * The Completing Axioms
 * Analysis; Cardinal Arithmetic; Abstract Theories
 * Further Strengthening of the Axiom System