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Axiomatic Set Theory

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Axiomatic Set Theory Cover

 

Synopses & Reviews

Publisher Comments:

This clear and well-developed approach to axiomatic set theory is geared toward upper-level undergraduates and graduate students. It examines the basic paradoxes and history of set theory and advanced topics such as relations and functions, equipollence, finite sets and cardinal numbers, rational and real numbers, and other subjects. 1960 edition.

Synopsis:

By means of the Zermelo-Fraenkel system, Suppes provides best treatment of axiomatic set theory on upper undergraduate and graduate levels. Topics include relations and functions, equipollence, finite sets and cardinal numbers, rational and real numbers, more

Synopsis:

Geared toward upper-level undergraduates and graduate students, this treatment examines the basic paradoxes and history of set theory and advanced topics such as relations and functions, equipollence, more. 1960 edition.

Synopsis:

In one of the finest treatments for upper undergraduate and graduate level students, Professor Suppes presents axiomatic set theory: the basic paradoxes and history of set theory, and advanced topics such as relations and functions, equipollence, finite sets and cardinal numbers, rational and real numbers and more. Exercises. References. Indexes.

Table of Contents

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 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. 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 Definition 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

Product Details

ISBN:
9780486616308
Author:
Suppes, Patrick
Publisher:
Dover Publications
Author:
Suppes, Patrick
Author:
Mathematics
Location:
New York
Subject:
General
Subject:
Mathematics
Subject:
Logic
Subject:
Set Theory
Subject:
Axiomatic set theory
Subject:
General Mathematics
Subject:
Mathematics-Logic and Philosophy
Copyright:
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Series Volume:
v. 13
Publication Date:
19720631
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
288
Dimensions:
8.5 x 38 in 0.67 lb

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Product details 288 pages Dover Publications - English 9780486616308 Reviews:
"Synopsis" by ,
By means of the Zermelo-Fraenkel system, Suppes provides best treatment of axiomatic set theory on upper undergraduate and graduate levels. Topics include relations and functions, equipollence, finite sets and cardinal numbers, rational and real numbers, more

"Synopsis" by ,
Geared toward upper-level undergraduates and graduate students, this treatment examines the basic paradoxes and history of set theory and advanced topics such as relations and functions, equipollence, more. 1960 edition.
"Synopsis" by ,
In one of the finest treatments for upper undergraduate and graduate level students, Professor Suppes presents axiomatic set theory: the basic paradoxes and history of set theory, and advanced topics such as relations and functions, equipollence, finite sets and cardinal numbers, rational and real numbers and more. Exercises. References. Indexes.

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