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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Résultats 1-5 sur 18
... Axiom Schema of Abstraction and Russell's Paradox 1.4 More Paradoxes 1.5 Preview of Axioms 2. GENERAL DEVELOPMENTS 2.1 Preliminaries: Formulas and Definitions 2.2 Axioms of Extensionality and Separation 2.3 Intersection, Union, and ...
... axioms: (i) The axiom of extensionality for sets, which asserts that two sets are identical if they have the same members; (ii) the axiom of abstraction, which states that given any property there exists a set whose members are just ...
... extensionality Axiom schema of separation Union axiom Pairing axiom Axiom of regularity Sum axiom Power set axiom Preview of Axioms.
... Axiom (V). I have never disguised from myself its lack of the selfevidence that belongs to the other axioms and that ... extension. May I always speak of the extension of a concept — speak of a class? And if not, how are the exceptional ...
... axiom schema of separation, should properly be formulated in the metalanguage. Such definition schemata will mainly occur in connection with the introduction of new methods of binding variables. We ... Axioms of Extensionality and Separation.
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 | |