The method of permutation models was introduced by Fraenkel in 1922 to prove the independence of the axiom of choice in set theory with atoms. We present a variant of the basic Fraenkel model in which supports are finite partitions of the set of atoms, rather than finite sets of atoms. Among our results are that, in this model, every well-ordered family of well-orderable sets has a choice function and that the union of such a family is well-orderable.

Author Bio

Ben Bruce, of Midland, MI, graduated from St. Olaf College in 2016, where he studied mathematics and philosophy. In his spare time, he enjoys playing the cello. This paper is the culmination of his work at the 2014 University of Michigan mathematics REU. Ben will begin graduate study in mathematics at the University of Wisconsin - Madison.