Book:Patrick Suppes/Axiomatic Set Theory/Second Edition

Subject Matter

 * Axiomatic Set Theory

Contents

 * Preface to the Dover Edition (Stanford, California: June, 1972)


 * Preface to the First Edition (Stanford, California: January, 1960)


 * 1.
 * 1.1 Set Theory and the Foundations of Mathematics
 * 1.2 Logic and Notation
 * 1.3 Axiom Schema of Abstraction and Russell's Paradox
 * 1.4 More Paradoxes
 * 1.5 Preview of Axioms


 * 2.
 * 2.1 Preliminaries: Formulas and Definitions
 * 2.2 Axioms of Extensionality and Separation
 * 2.3 Intersection, Union, and Difference of Sets
 * 2.4 Pairing Axiom and Ordered Pairs
 * 2.5 Definition by Abstraction
 * 2.6 Sum Axiom and Families of Sets
 * 2.7 Power Set Axiom
 * 2.8 Cartesian Product of Sets
 * 2.9 Axiom of Regularity
 * 2.10 Summary of Axioms


 * 3.
 * 3.1 Operations on Binary Relations
 * 3.2 Ordering Relations
 * 3.3 Equivalence Relations and Partitions
 * 3.4 Functions


 * 4.
 * 4.1 Equipollence
 * 4.2 Finite Sets
 * 4.3 Cardinal Numbers
 * 4.4 Finite Cardinals


 * 5.
 * 5.1 Definitions and General Properties of Ordinals
 * 5.2 Finite Ordinals and Recursive Definitions
 * 5.3 Denumerable Sets


 * 6.
 * 6.1 Introduction
 * 6.2 Fractions
 * 6.3 Non-negative Rational Numbers
 * 6.4 Rational Numbers
 * 6.5 Cauchy Sequences of Rational Numbers
 * 6.6 Real Numbers
 * 6.7 Sets of the Power of the Continuum


 * 7.
 * 7.1 Transfinite Induction and Definition by Transfinite Recursion
 * 7.2 Elements of Ordinal Arithmetic
 * 7.3 Cardinal Numbers Again and Alephs
 * 7.4 Well-Ordered Sets
 * 7.5 Revised Summary of Axioms


 * 8.
 * 8.1 Some Applications of the Axiom of Choice
 * 8.2 Equivalents of the Axiom of Choice
 * 8.3 Axioms Which Imply the Axiom of Choice
 * 8.4 Independence of the Axiom of Choice and the Generalized Continuum Hypothesis











Source work progress
* : $\S 1.3$ Axiom Schema of Abstraction and Russell's Paradox


 * redo from start