Axiomatic Set TheoryCourier Corporation, 1 janv. 1972 - 267 pages 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. |
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Table des matières
INTRODUCTION | 1 |
GENERAL DEVELOPMENTS | 14 |
RELATIONS AND FUNCTIONS | 57 |
EQUIPOLLENCE FINITE SETS AND CARDINAL NUMBERS | 91 |
FINITE ORDINALS AND DENUMERABLE SETS | 127 |
RATIONAL NUMBERS AND REAL NUMBERS | 159 |
TRANSFINITE INDUCTION AND ORDINAL ARITHMETIC | 195 |
THE AXIOM OF CHOICE | 239 |
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Expressions et termes fréquents
asserts axiom for cardinals axiom of choice axiom of extensionality axiom of regularity axiom schema cardinal numbers Cauchy sequence Chapter continuum Dedekind infinite define domain empty set equipollent equivalence relation exercise finite cardinal finite sets formulation fractions function f given infinite set integer introduced intuitive limit ordinal logic mathematics maximal element multiplication natural numbers non-negative rational numbers notation notion object language obvious ordered pairs ordinal addition ordinal arithmetic paradox partition primitive formula proof of Theorem Prove Theorem Q.E.D. THEOREM real numbers schema of replacement schema of separation sequence of real sequences of rational set of real similar special axiom strict simple ordering Suppose Tarski Theorem 12 Theorem 27 Theorem 55 THEOREM SCHEMA transfinite cardinal transfinite induction transfinite recursion unique upper bound variables virtue of Theorem well-ordered sets whence Zermelo Zermelo-Fraenkel set theory