具有非同构超幂的II_1因子
II_1 factors with non-isomorphic ultrapowers
摘要：
我们证明了存在不可数多个可分的II $_1$因子，其超幂（相对于任意超滤子）是非同构的。事实上，我们证明，家庭的非同构II $_1$因素最初介绍了麦克达夫\cite{MD69a,MD69b}是这样的例子。这就需要存在一个连续的非elementarily等价的II $_1$因素，从而解决了一个著名的开放问题，在连续模型论的算子代数。
英文摘要：
We prove that there exist uncountably many separable II$_1$ factors whose ultrapowers (with respect to arbitrary ultrafilters) are non-isomorphic. In fact, we prove that the families of non-isomorphic II$_1$ factors originally introduced by McDuff \cite{MD69a,MD69b} are such examples. This entails the existence of a continuum of non-elementarily equivalent II$_1$ factors, thus settling a well-known open problem in the continuous model theory of operator algebras.
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