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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... 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 symbol ...
... axiom schema of replacement is introduced in connection with establishing an ... axiom of choice and its equivalents, like Hausdorff's Maximal Principle and Zorn's Lemma. Important facts whose ... cardinals. The material in the first six.
... Axiom Schema of Abstraction and Russell's Paradox 1.4 More Paradoxes 1.5 ... Axiom and Ordered Pairs 2.5 Definition by Abstraction 2.6 Sum Axiom and Families ... Cardinals 5. FINITE ORDINALS AND DENUMERABLE SETS 5.1 Definition and General ...
... Cardinal Numbers Again and Alephs 7.4 Well-Ordered Sets 7.5 Revised Summary of Axioms 8. THE AXIOM OF CHOICE 8.1 Some Applications of the Axiom of Choice 8.2 Equivalents of the Axiom of Choice 8.3 Axioms Which Imply the Axiom of Choice ...
... cardinal numbers, infinite sets, ordinal arithmetic, transfinite induction, definition by transfinite recursion, axiom of choice, Zorn's Lemma. At this point the reader is not expected to know what these phrases mean, but such a list ...
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 | |