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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... define the real numbers. Most of the elementary facts about sets of the power of the continuum are proved in the final section. Because for many courses in set theory it will not be feasible in the time allotted to include the ...
... define real numbers; let E be the remaining subsequence. Translating and paraphrasing somewhat, we may use Richard's original formulation to define a certain real number N with respect to E: “The real number whose whole part is zero ...
... define such formulas so that merely by looking at the form of an expression we can automatically decide in a finite number of steps whether or not it is a primitive formula. Although this definition is purely syntactical or structural ...
... definition for any exactly stated mathematical theory is to provide rules of definition whose satisfaction entails satisfaction of the two criteria just stated. We may restrict ourselves here to rules for defining operation symbols ...
... definition which is an identity we have the following rule. An identity P introducing a new n-place operation symbol O is a proper definition if and only if P is ... definition in arithmetic is provided by a definition of division, for which.
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 | |