论文标题
关于奇特冯·诺伊曼代数的模型理论的调查
A survey on the model theory of tracial von Neumann algebras
论文作者
论文摘要
我们调查了过去15年中发生的奇特冯·诺伊曼代数的模型理论中的发展。我们讨论了适当的一阶语言，用于使该课程以及II $ _1 $因子的子类。我们讨论了如何使用模型理论思想来解决围绕奇怪的超能力的同构，von neumann代数相对于不同的超级滤器，然后再继续进行更多的模型理论问题，例如II $ _1 $ $ _1 $因素的理论和现有关闭的II $ _1 $ _1 $ _1 $因素。我们最终以模型理论思想在相对换向因素的问题上进行了两个最新应用。
We survey the developments in the model theory of tracial von Neumann algebras that have taken place in the last fifteen years. We discuss the appropriate first-order language for axiomatizing this class as well as the subclass of II$_1$ factors. We discuss how model-theoretic ideas were used to settle a variety of questions around isomorphism of ultrapowers of tracial von Neumann algebras with respect to different ultrafilters before moving on to more model-theoretic concerns, such as theories of II$_1$ factors and existentially closed II$_1$ factors. We conclude with two recent applications of model-theoretic ideas to questions around relative commutants.
