论文标题
在高铁II_1因子理论的小片段中表达的属性
Properties expressible in small fragments of the theory of the hyperfinite II_1 factor
论文作者
论文摘要
我们表明，任何具有与高限量II $ _1 $ altion $ \ Mathcal {r} $具有相同4量词理论的II $ _1 $因子都可以满足Popa fortorial通勤嵌入问题（FCEP）的结论，并且具有棕色财产。这些结果改善了最新结果，证明了在更强的假设中得出相同的结论，即该因子实际上基本上等同于$ \ Mathcal {r} $。本着同样的精神，我们改善了名字命名作者的最新结果，他表明，如果（1）（1）可包含的可嵌入因子的免费产品（t）基础上的可包含因子的免费产品再次可嵌入，并且（2）$ \ Mathcal {r} $是无限的一般性嵌入式因子，则FCEP是所有属性的真实属性。在本文中，可以证明可以削弱项目（2），以假设$ \ Mathcal {r} $具有与无限通用的可嵌入因子相同的3量化器理论。
We show that any II$_1$ factor that has the same 4-quantifier theory as the hyperfinite II$_1$ factor $\mathcal{R}$ satisfies the conclusion of the Popa Factorial Commutant Embedding Problem (FCEP) and has the Brown property. These results improve recent results proving the same conclusions under the stronger assumption that the factor is actually elementarily equivalent to $\mathcal{R}$. In the same spirit, we improve a recent result of the first-named author, who showed that if (1) the amalgamated free product of embeddable factors over a property (T) base is once again embeddable, and (2) $\mathcal{R}$ is an infinitely generic embeddable factor, then the FCEP is true of all property (T) factors. In this paper, it is shown that item (2) can be weakened to assume that $\mathcal{R}$ has the same 3-quantifier theory as an infinitely generic embeddable factor.
