  Recently, Boutonnet, Chifan, and Ioana proved that McDuff's family of
continuum many pairwise nonisomorphic separable II$_1$ factors are in fact
pairwise non-elementarily equivalent by proving that any ultrapowers of two
distinct members of the family are nonsiomorphic. We use Ehrenfeucht-Fraisse
games to provide an upper bound on the quantifier-depth of sentences which
distinguish these theories.
