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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... transfinite induction and ordinal arithmetic. The treatment of transfinite induction and definition by transfinite recursion is one of the most detailed in print. Numerous variant formulations have been given in the hope that successive ...
... TRANSFINITE INDUCTION AND ORDINAL ARITHMETIC 7.1 Transfinite Induction and Definition by Transfinite Recursion 7.2 Elements of Ordinal Arithmetic 7.3 Cardinal Numbers Again and Alephs 7.4 Well-Ordered Sets 7.5 Revised Summary of Axioms ...
... 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 may still give a clue to the more detailed contents 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 | |