# Book:Patrick Suppes/Axiomatic Set Theory/Second Edition

Jump to navigation
Jump to search
## Patrick Suppes:

## Contents

## Patrick Suppes: *Axiomatic Set Theory (2nd Edition)*

Published $\text {1972}$, **Dover Publications**

- ISBN 0-486-61630-4.

### Subject Matter

### Contents

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

- Preface to the Dover Edition (

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

- Preface to the First Edition (

- 1. introduction
- 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. general developments
- 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 Families of Sets
- 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. relations and functions
- 3.1 Operations on Binary Relations
- 3.2 Ordering Relations
- 3.3 Equivalence Relations and Partitions
- 3.4 Functions

- 4. equipollence, finite sets, and cardinal numbers
- 4.1 Equipollence
- 4.2 Finite Sets
- 4.3 Cardinal Numbers
- 4.4 Finite Cardinals

- 5. finite ordinals and denumerable sets
- 5.1 Definitions and General Properties of Ordinals
- 5.2 Finite Ordinals and Recursive Definitions
- 5.3 Denumerable Sets

- 6. rational numbers and real numbers
- 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. transfinite induction and ordinal arithmetic
- 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. the axiom of choice
- 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

- References

- Glossary of Symbols

- Author Index

- Subject Index

## Further Editions

## Source work progress

- 1972: Patrick Suppes:
*Axiomatic Set Theory*(2nd ed.) ... (previous) ... (next): $\S 1.3$ Axiom Schema of Abstraction and Russell's Paradox

- redo from start