English

Uniformly Super McDuff II$_1$ Factors

Operator Algebras 2023-03-07 v1 Logic

Abstract

We introduce and study the family of uniformly super McDuff II1_1 factors. This family is shown to be closed under elementary equivalence and also coincides with the family of II1_1 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 II1_1 factors are uniformly super McDuff. Lastly, we investigate when finitely generic II1_1 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

R2 v1 2026-06-28T09:02:28.390Z