The theory of tracial von Neumann algebras does not have a model companion
نویسندگان
چکیده
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 modelcomplete theory of II1 factors.
منابع مشابه
The Theory of Tracial Von Neumann Algebras Does Not Have a Model Companion
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 modelcomplete theory of II1 factors.
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ورودعنوان ژورنال:
- J. Symb. Log.
دوره 78 شماره
صفحات -
تاریخ انتشار 2013