We examine the properties of existentially closed (-embeddable) II₁ factors. In particular, we use the fact that every automorphism of an existentially closed (-embeddable) II₁ factor is approximately inner to prove that Th() is not model-complete. We also show that Th() 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().
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm126-12-2015,
author = {Ilijas Farah and Isaac Goldbring and Bradd Hart and David Sherman},
title = {Existentially closed II1 factors},
journal = {Fundamenta Mathematicae},
volume = {233},
year = {2016},
pages = {173-196},
zbl = {06575009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm126-12-2015}
}
Ilijas Farah; Isaac Goldbring; Bradd Hart; David Sherman. Existentially closed II₁ factors. Fundamenta Mathematicae, Tome 233 (2016) pp. 173-196. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm126-12-2015/