# Accession Number:

## AD0655086

# Title:

## FINITE VERSIONS OF THE AXIOM OF CHOICE,

# Descriptive Note:

# Corporate Author:

## NEW YORK UNIV N Y SCHOOL OF ENGINEERING AND SCIENCE

# Personal Author(s):

# Report Date:

## 1967-06-01

# Pagination or Media Count:

## 117.0

# Abstract:

We consider A. Mostowskis 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 Mostowskis 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 mun, 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 mun in relation to the axioms of choice for finite sets are obtained by consideration of modified versions of Bertrands Postulate. Some of the independence theorems are obtained by constructing Fraenkel-Mostowski-type models for set theory. Author

# Descriptors:

# Subject Categories:

- Theoretical Mathematics