Games and elementary equivalence of II$_1$-factors

Isaac Goldbring and Thomas Sinclair

Vol. 278 (2015), No. 1, 103–118

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.

Keywords

II$_1$-factors, model theory, Ehrenfeucht–Fraïssé games

Mathematical Subject Classification 2010

Primary: 46L10

Secondary: 03C20

Milestones

Received: 19 August 2014

Revised: 2 March 2015

Accepted: 4 March 2015

Published: 30 September 2015