 The Fraenkel model arises if H is the group of all permutations of an infinite set A. In the Fraenkel model the set A is infinite but Dedekind-finite (i.e., A has no one-one function into a proper subset) and cannot be well-ordered, not even linearly ordered. Moreover, the set A is not the disjoint union of two infinite sets. There is no choice function for two element subsets of A.