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arXiv · 1406.5242

Games and elementary equivalence of $\rm II_1$ factors

Isaac Goldbring·Thomas Sinclair
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Abstract

We use Ehrenfeucht-Fra\"iss\'e 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.

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Isaac Goldbring, Thomas Sinclair. 2014-06-19. Games and elementary equivalence of $\rm II_1$ factors. https://doi.org/10.2140/pjm.2015.278.103

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