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

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  • 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).


  • Farah, Ilijas
  • Goldbring, Isaac
  • Hart, Bradd
  • Sherman, David

publication date

  • January 1, 2016