On the theories of McDuff's II$_1$ factors
Logic
2016-02-05 v1 Operator Algebras
Abstract
Recently, Boutonnet, Chifan, and Ioana proved that McDuff's family of continuum many pairwise nonisomorphic separable II factors are in fact pairwise non-elementarily equivalent by proving that any ultrapowers of two distinct members of the family are nonsiomorphic. We use Ehrenfeucht-Fraisse games to provide an upper bound on the quantifier-depth of sentences which distinguish these theories.
Keywords
Cite
@article{arxiv.1602.01817,
title = {On the theories of McDuff's II$_1$ factors},
author = {Isaac Goldbring and Bradd Hart},
journal= {arXiv preprint arXiv:1602.01817},
year = {2016}
}
Comments
14 pages