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ENFORCEABLE OPERATOR ALGEBRAS
- Part of
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- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 20 / Issue 1 / January 2021
- Published online by Cambridge University Press:
- 01 March 2019, pp. 31-63
- Print publication:
- January 2021
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- Article
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- You have access
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We adapt the classical notion of building models by games to the setting of continuous model theory. As an application, we study to what extent canonical operator algebras are enforceable models. For example, we show that the hyperfinite II1 factor is an enforceable II1 factor if and only if the Connes Embedding Problem has a positive solution. We also show that the set of continuous functions on the pseudoarc is an enforceable model of the theory of unital, projectionless, abelian
$\text{C}^{\ast }$-algebras and use this to show that it is the prime model of its theory.
