Partial choice functions for families of finite sets
by Hall and Shelah. [HalSh:934]
Fundamenta Math, 2013
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
. 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.
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