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arXiv · 1310.5138

Existentially closed II_1 factors

Ilijas Farah·Isaac Goldbring·Bradd Hart·David Sherman
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Abstract

We examine the properties of existentially closed (R^omega-embeddable) II_1 factors. In particular, we use the fact that every automorphism of an existentially closed (R^omega-embeddable) II_1 factor is approximately inner to prove that Th(R) is not model-complete. We also show that Th(R) is complete for both finite and infinite forcing and use the latter result to prove that there exist continuum many nonisomorphic existentially closed models of Th(R).

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Ilijas Farah, Isaac Goldbring, Bradd Hart, David Sherman. 2013-10-18. Existentially closed II_1 factors. https://arxiv.org/abs/1310.5138

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