Games and elementary equivalence of $\rm II_1$ factors
Logic
2016-01-20 v2 Operator Algebras
Abstract
We use Ehrenfeucht-Fra\"iss\'e games to give a local geometric criterion for elementary equivalence of II factors. We obtain as a corollary that two II factors are elementarily equivalent if and only their unitary groups are elementarily equivalent as -metric spaces.
Keywords
Cite
@article{arxiv.1406.5242,
title = {Games and elementary equivalence of $\rm II_1$ factors},
author = {Isaac Goldbring and Thomas Sinclair},
journal= {arXiv preprint arXiv:1406.5242},
year = {2016}
}
Comments
13 pages; final version to appear in the Pacific Journal of Mathematics