# A ug 2 00 8 Partial choice functions for families of finite sets

@inproceedings{Hall2008AU2, title={A ug 2 00 8 Partial choice functions for families of finite sets}, author={Eric Joseph Hall and Saharon Shelah}, year={2008} }

- Published 2008

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 (FraenkelMostowski) model in which the set of atoms has the structure of a vector space over the field of p elements, and then the use of atoms is eliminated by citing an embedding theorem… CONTINUE READING

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