We deal with weak choice principles of the form: Every "finite" family of non-empty sets has a choice function, where "finite" stands for one of several different definitions of finiteness that are not equivalent unless we assume the axiom of choice (AC). Several relations of implication and independence are established. In the process, we answer a few open questions about the relations between different definitions of finiteness.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm173-1-4,
author = {Omar De la Cruz},
title = {Finiteness and choice},
journal = {Fundamenta Mathematicae},
volume = {173},
year = {2002},
pages = {57-76},
zbl = {0994.03041},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm173-1-4}
}
Omar De la Cruz. Finiteness and choice. Fundamenta Mathematicae, Tome 173 (2002) pp. 57-76. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm173-1-4/