Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Choices from finite sets and choices of finite subsets


Author: Martin M. Zuckerman
Journal: Proc. Amer. Math. Soc. 27 (1971), 133-138
MSC: Primary 02.60
DOI: https://doi.org/10.1090/S0002-9939-1971-0270905-5
MathSciNet review: 0270905
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In set theory without the axiom of choice we prove a consistency result involving certain ``finite versions'' of the axiom of choice. Assume that it is possible to select a nonempty finite subset from each nonempty set. We determine sets $ Z$, of integers, which have the property that $ n \in Z$ is a necessary and sufficient condition for the possibility of choosing an element from every $ n$-element set. Given any nonempty set $ P$ of primes, the set $ {Z_p}$, consisting of integers which are not ``linear combinations'' of primes of $ P$, is such a set $ Z$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 02.60

Retrieve articles in all journals with MSC: 02.60


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0270905-5
Keywords: Axiom of choice for $ n$-element sets, multiple choice axioms, Fraenkel-Mostowski models, relative consistency
Article copyright: © Copyright 1971 American Mathematical Society

American Mathematical Society