Existentially closed II_1 factors
Operator Algebras
2013-10-21 v1 Logic
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).
Cite
@article{arxiv.1310.5138,
title = {Existentially closed II_1 factors},
author = {Ilijas Farah and Isaac Goldbring and Bradd Hart and David Sherman},
journal= {arXiv preprint arXiv:1310.5138},
year = {2013}
}
Comments
22 pages