Explicit sentences distinguishing Mcduff’s II1 factors

Recently, Boutonnet, Chifan, and Ioana proved that McDuff’s examples of continuum many pairwise non-isomorphic separable II1 factors are in fact pairwise non-elementarily equivalent. Their proof proceeded by showing that any ultrapowers of any two distinct McDuff examples are not isomorphic. In a paper by the first two authors of this paper, Ehrenfeucht–Fra¨ısse games were used to find an upper bound on the quantifier complexity of sentences …