Accession Number : AD0655086

Title :   FINITE VERSIONS OF THE AXIOM OF CHOICE,

Corporate Author : NEW YORK UNIV N Y SCHOOL OF ENGINEERING AND SCIENCE

Personal Author(s) : Zuckerman,Martin Michael

Report Date : JUN 1967

Pagination or Media Count : 117

Abstract : We consider A. Mostowski's axioms of choice for finite sets, (n), which state that for every set X whose elements are n-element sets, there is a function fX such that fX (x) epsilon X for each x epsilon X. We extend some of Mostowski's results concerning necessary (respectively, sufficient) conditions for implications of the form ((m1) and (m2) and ... and (mk)) approaches (n), and we introduce some new necessary (respectively, sufficient) conditions for this implication. Some of these results are in terms of an associated number-theoretic function mu(n), defined for integers n = or > 2 as the greatest prime p such that n is expressible as the sum of primes not less than p. Properties of mu(n) in relation to the axioms of choice for finite sets are obtained by consideration of modified versions of Bertrand's Postulate. Some of the independence theorems are obtained by constructing Fraenkel-Mostowski-type models for set theory. (Author)

Descriptors :   (*SET THEORY, NUMBERS), MATHEMATICS, THEOREMS, THESES

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE