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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... correspond to several English idioms. Thus (∀v)P may be read For all v, P as well as For every v, P. Sentences (1) and (2) illustrate the use of parentheses for purposes of punctuation. No formal explanation seems necessary. However ...
... corresponding set of things having that property. In considering how to build anew the foundations of set theory, perhaps the first thing to notice is that the axiom of abstraction is really an infinite bundle of axioms rather than a ...
... correspond very closely to those in Zermelo [1908]. However, when we come to the theory of transfinite induction and ordinal arithmetic, we shall need to add a stronger axiom schema than that of separation, namely, what is usually ...
... 0 → x = y · z) & (y = 0 → z = 0). The corresponding natural choice in set theory is the empty set. Thus any conditional definition satisfying the rule stated above may be converted into a proper definition by writing it as: In.
... corresponds in the language of logic to introducing a free variable in a premise (in this case the premise: x ∈ A). We now define proper inclusion. DEFINITION 4. A ⊂ B ↔ A ⊆ B & A ≠ B. Thus using informally the braces notation not ...
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 | |