Axiomatic Set TheoryCourier Corporation, 4 mai 2012 - 265 pages One of the most pressingproblems of mathematics over the last hundred years has been the question: What is a number? One of the most impressive answers has been the axiomatic development of set theory. The question raised is: "Exactly what assumptions, beyond those of elementary logic, are required as a basis for modern mathematics?" Answering this question by means of the Zermelo-Fraenkel system, Professor Suppes' coverage is the best treatment of axiomatic set theory for the mathematics student on the upper undergraduate or graduate level. |
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... special axiom to the effect that the cardinal numbers of two equipollent sets are identical. This axiom is not part of the standard Zermelo-Fraenkel system, and so every definition or theorem which depends on it has been marked by the ...
... axioms are introduced. In Chapter 4, a special axiom for cardinal numbers is presented and used mainly in the context of that chapter. This special axiom is not a part of classical Zermelo-Fraenkel set theory, but it enormously ...
... axiom schema of separation: (∃C)(∀x)(x ∈x ∈ A & x ∈ B). We now need to show that C is unique. Suppose there were a second set C′ such that for every x x ∈ C′ ↔ x ∈ A & x ∈ B; then for every x x ∈ C′ ↔ x ∈ C and by virtue of ...
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Table des matières
RELATIONS AND FUNCTIONS | |
EQUIPOLLENCE FINITE SETS AND CARDINAL NUMBERS | |
FINITE ORDINALS AND DENUMERABLE SETS | |
RATIONAL NUMBERS AND REAL NUMBERS | |
TRANSFINITE INDUCTION AND ORDINAL ARITHMETIC | |
THE AXIOM OF CHOICE | |
REFERENCES | |
AUTHOR INDEX | |