Sh:934
- Hall, E. J., & Shelah, S. (2013). Partial choice functions for families of finite sets. Fund. Math., 220(3), 207–216. arXiv: 0808.0535 DOI: 10.4064/fm220-3-2 MR: 3040670
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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. - Version 2013-02-03_11 (10p) 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},
mrnumber = {3040670},
mrclass = {03E25},
doi = {10.4064/fm220-3-2},
note = {\href{https://arxiv.org/abs/0808.0535}{arXiv: 0808.0535}},
arxiv_number = {0808.0535}
}