Games and elementary equivalence of $\rm II_1$ factors
arXiv:1406.5242 · doi:10.2140/pjm.2015.278.103
Abstract
We use Ehrenfeucht-Fraïssé games to give a local geometric criterion for elementary equivalence of II$_1$ factors. We obtain as a corollary that two II$_1$ factors are elementarily equivalent if and only their unitary groups are elementarily equivalent as $\mathbb Z_4$-metric spaces.
13 pages; final version to appear in the Pacific Journal of Mathematics