# Existentially closed ${\rm II}_1$ factors Academic Article

•
• Overview
•
• Research
•
• Identity
•
•
• View All
•

### 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).

### authors

• Farah, Ilijas
• Goldbring, Isaac