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Book Cover
Book
Author Suppes, Patrick, 1922-2014.

Title Axiomatic set theory / by Patrick Suppes
Published New York : Dover Publications, [1972]

Copies

Location Call no. Vol. Availability
 W'PONDS  511.3 Sup  AVAILABLE
Description xii, 267 pages ; 22 cm
Series University series in undergraduate mathematics
University series in undergraduate mathematics.
Contents Machine derived contents note: 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
Analysis Mathematics Sets Axiomatic theories
Notes Reprint of the 1960 ed., issued in series: The University series in undergraduate mathematics
Bibliography Bibliography: pages 255-258
Subject Set theory.
Axiomatic set theory.
Set theory.
LC no. 72086226
ISBN 0486616304