# Sh:934

• Hall, E. J., & Shelah, S. (2013). Partial choice functions for families of finite sets. Fund. Math., 220(3), 207–216.
• Abstract:
Let p be a prime. We show that ZF + “Every countable set of p-element sets has an infinite partial choice function” is not strong enough to prove that every countable set of p-element sets has a choice function, answering an open question from [1]. The independence result is obtained by way of a permutation (Fraenkel-Mostowski) model in which the set of atoms has the structure of a vector space over the field of p elements. By way of comparison, some simpler permutation models are considered in which some countable families of p-element sets fail to have infinite partial choice functions.
• published version (10p)
Bib entry
@article{Sh:934,
author = {Hall, Eric Jonathan and Shelah, Saharon},
title = {{Partial choice functions for families of finite sets}},
journal = {Fund. Math.},
fjournal = {Fundamenta Mathematicae},
volume = {220},
number = {3},
year = {2013},
pages = {207--216},
issn = {0016-2736},
doi = {10.4064/fm220-3-2},
mrclass = {03E25},
mrnumber = {3040670},
mrreviewer = {Paul E. Howard},
doi = {10.4064/fm220-3-2},
note = {\href{https://arxiv.org/abs/0808.0535}{arXiv: 0808.0535}},
arxiv_number = {0808.0535}
}