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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... ordinal addition. The more familiar facts about alephs and well-ordered sets are proved in the latter part of the chapter. Chapter 8 deals mainly with the axiom of choice and its equivalents, like Hausdorff's Maximal Principle and ...
... construction like that of separation is required, but instead a finite ... ordinal numbers and the class of all sets both exist, but both are proper ... Sum axiom Power set axiom Preview of Axioms.
... construction of the real numbers, and no further axioms are needed for this work. In Chapter 7 the axiom schema of replacement is brought in as necessary for the development of ordinal arithmetic and transfinite induction. It is also ...
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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 | |