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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... integers, rational numbers and real numbers has been a central problem for the classical researches of Weierstrass, Dedekind, Kronecker, Frege, Peano, Russell, Whitehead, Brouwer, and others. Perplexities about the nature of number did ...
... integers). In 1878 he introduced the fundamental notion of two sets being equipollent or having the same power (Mächtigkeit) if they can be put into one-one correspondence with each other. Clearly two finite sets have the same power ...
... integers, the sentence '7∈A' is true and '6∈A' is false. Using '∈' and the logical notation introduced in the previous section, we may give a precise formulation of the axiom of abstraction: where it is understood that φ(x) is a ...
... integer variables ranging over non-negative integers ('m', 'n', 'p', ...), rational variables ranging over non-negative rational numbers ('M', 'N', 'P', ...). We shall not explicitly consider rules for definition schemata which ...
... integer} = {2,3}. It should be clear why use of this notation is called definition by abstraction. We begin by considering some property, such as being greater than , and abstract from this property the set of all entities having the ...
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 | |