Define a Russell socks set as a countable set of (pairwise disjoint) pairs such that no infinite subset has a choice function. Of course, if ZFC is consistent then it proves that no such set exists (as the axiom of choice is precisely the statement that every set has a choice function). On the other hand, it is known to be consistent with ZF that such a set exists.
Many wonderful and entertaining consequences of such a set existing in a model of ZF can be found in papers such as 'On the number of Russell's socks [...]' by Herrlich and Tachtsis or in Ethan Thomas' undergraduate thesis on the subject.
Neither of these papers explicitly construct a model of ZF containing a Russell socks set. Are any of the more common models such as Cohen's known to contain such a set? Is it easy to construct a model containing one?
Any reference would be much appreciated!