Uniformly Super McDuff II$_1$ Factors
Operator Algebras
2023-03-07 v1 Logic
Abstract
We introduce and study the family of uniformly super McDuff II factors. This family is shown to be closed under elementary equivalence and also coincides with the family of II factors with the Brown property introduced in arXiv:2004.02293. We show that a certain family of existentially closed factors, the so-called infinitely generic factors, are uniformly super McDuff, thereby improving a recent result of arXiv:2205.07442. We also show that Popa's family of strongly McDuff II factors are uniformly super McDuff. Lastly, we investigate when finitely generic II factors are uniformly super McDuff.
Cite
@article{arxiv.2303.02809,
title = {Uniformly Super McDuff II$_1$ Factors},
author = {Isaac Goldbring and David Jekel and Srivatsav Kunnawalkam Elayavalli and Jennifer Pi},
journal= {arXiv preprint arXiv:2303.02809},
year = {2023}
}
Comments
22 pages. Comments are welcome