Axiomatic Set Theory

Produktbeschreibung

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. 

Inhaltsverzeichnis

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