# 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 -
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} }