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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... unique place: with a few rare exceptions the entities which are studied and analyzed in mathematics may be regarded as certain particular sets or classes of objects.* This means that the various branches of mathematics may be formally ...
... unique object. For a definition which is an identity we have the following rule. An identity P introducing a new n-place operation symbol O is a proper definition if and only if P is of the form O(v1,...vn) = are primitive symbols and ...
... 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 the axiom of extensionality DEFINITION 5. A ∩ B = y ↔ (∀x)(x ∈ y ↔ x ∈ A & x ∈ B ...
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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 | |