The Theory of Tracial Von Neumann Algebras Does Not Have A Model Companion
The Theory of Tracial Von Neumann Algebras Does Not Have A Model Companion
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追踪冯·诺依曼代数理论没有模型伴侣
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Thomas Sinclair
中科院分区：
文献类型：
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作者：
Isaac Goldbring;B. Hart;Thomas Sinclair
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，即任何局部普遍的理论，McDuff II 1因子没有量词消除。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II1因素。
Abstract 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 II1 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 II1 factors.