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 schema of replacement is introduced in connection with establishing an appropriate recursion schema to define ordinal addition. The more familiar facts about alephs and well-ordered sets are proved in the latter part of the ...
... 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 and theorems, any universal quantifier whose scope is the whole formula. For instance, instead of (1) above, we would write: (∃y) (x < y). In a few places we shall need the ... Axiom Schema of Abstraction and Russell's Paradox. In.
Patrick Suppes. § 1.3 Axiom Schema of Abstraction and Russell's Paradox. In his initial development of set theory, Cantor did not work explicitly from axioms. However, analysis of his proofs indicates that almost all of the theorems ...
... axiom we have granted too much. If we adhere to ordinary logic we cannot in a self-consistent manner claim that for ... schema. The reason for using the word 'schema' should be obvious. As it stands (1) is not a definite assertion, but a ...
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 | |