
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 nelement 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 numbertheoretic 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 FraenkelMostowskitype models for set theory. (Author)
Descriptors : (*SET THEORY, NUMBERS), MATHEMATICS, THEOREMS, THESES
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE