Explicit sentences distinguishing McDuff's II$_1$ factors
Logic
2017-01-30 v1 Operator Algebras
Abstract
Recently, Boutonnet, Chifan, and Ioana proved that McDuff's examples of continuum many pairwise non-isomorphic separable II factors are in fact pairwise non-elementarily equivalent. Their proof proceeded by showing that any ultrapowers of any two distinct McDuff examples are not isomorphic. In a paper by the first two authors of this paper, Ehrenfeucht-Fra\"isse games were used to find an upper bound on the quantifier complexity of sentences distinguishing the McDuff examples, leaving it as an open question to find concrete sentences distinguishing the McDuff factors. In this paper, we answer this question by providing such concrete sentences.
Keywords
Cite
@article{arxiv.1701.07928,
title = {Explicit sentences distinguishing McDuff's II$_1$ factors},
author = {Isaac Goldbring and Bradd Hart and Henry Towsner},
journal= {arXiv preprint arXiv:1701.07928},
year = {2017}
}
Comments
10 pages