跟踪von Neumann algebras理论没有一个模型伴侣
The theory of tracial von Neumann algebras does not have a model companion
摘要：
本文证明了迹von Neumann代数理论没有模伴。这将遵循这样的事实，即任何局部普遍的McDuff II_1因子的理论没有量词消除。我们还展示了如何一个积极的解决方案，康纳斯嵌入问题意味着，不可能有模型完整的理论II_1因素。
英文摘要：
In this note, we show that the theory of tracial von Neumann algebras does not have a model companion. This will follow from the fact that the theory of any locally universal, McDuff II_1 factor does not have quantifier elimination. We also show how a positive solution to the Connes Embedding Problem implies that there can be no model-complete theory of II_1 factors.
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