一致超McDuff II $_1$因子
Uniformly Super McDuff II$_1$ Factors
摘要：
引入并研究了一致超McDuff II $_1$因子族.这个家庭被证明是封闭的初等等价下，也符合家庭的II $_1$因素与布朗属性中介绍arXiv：2004.02293。我们证明了一个存在闭因子族，即所谓的无限泛因子，是一致超McDuff的，从而改进了arXiv：2205.07442的一个最近结果。我们还证明了Popa族的强McDuff II $_1$因子是一致超McDuff的.最后，我们调查时，通用II $_1$因素是一致的超级McDuff。
英文摘要：
We introduce and study the family of uniformly super McDuff II$_1$ factors. This family is shown to be closed under elementary equivalence and also coincides with the family of II$_1$ 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 II$_1$ factors are uniformly super McDuff. Lastly, we investigate when finitely generic II$_1$ factors are uniformly super McDuff.
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