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Preprint Number 638

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638. Ilijas Farah, Isaac Goldbring, Bradd Hart, and David Sherman
Existentially closed II_1 factors

Submission date: 18 October 2013


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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Full text arXiv 1310.5138: pdf, ps.

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