算子代数III的模型论：初等等价和II_1因子
Model theory of operator algebras III: Elementary equivalence and II_1 factors
摘要：
利用连续模型论得到了II_1因子及其超幂之间的同构和嵌入的若干结果。除此之外，我们证明了对于任意II_1因子M，存在连续统许多非同构的可分II_1因子，它们的超幂同构于M的超幂。我们还给出了Connes嵌入问题的穷人解决方案：存在一个可分的II_1因子，使得所有的II_1因子嵌入到它的一个超幂中.
英文摘要：
We use continuous model theory to obtain several results concerning isomorphisms and embeddings between II_1 factors and their ultrapowers. Among other things, we show that for any II_1 factor M, there are continuum many nonisomorphic separable II_1 factors that have an ultrapower isomorphic to an ultrapower of M. We also give a poor man's resolution of the Connes Embedding Problem: there exists a separable II_1 factor such that all II_1 factors embed into one of its ultrapowers.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
