Submission date: 19 June 2014.

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 Z_4-metric spaces.

Mathematics Subject Classification:

Keywords and phrases: Ehrenfeucht-Fraïssé games, II_1 factors

Full text arXiv 1406.5242: pdf, ps.