On the theories of McDuff's II₁ factors

2016/02/04 by Goldbring, Isaac, Hart, Bradd
#FOS: Mathematics #Logic (math.LO) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1602.01817

Abstract

Recently, Boutonnet, Chifan, and Ioana proved that McDuff's family of continuum many pairwise nonisomorphic separable II₁ factors are in fact pairwise non-elementarily equivalent by proving that any ultrapowers of two distinct members of the family are nonsiomorphic. We use Ehrenfeucht-Fraisse games to provide an upper bound on the quantifier-depth of sentences which distinguish these theories.

Related

• Explicit sentences distinguishing McDuff's II₁ factors
• Uniformly Super McDuff II₁ Factors
• Constructing strongly equivalent nonisomorphic models for unsuperstable theories, Part A
• Elementary embeddings into ultrapower II₁ factors without a UCP lift
• Non-embeddable II₁ factors resembling the hyperfinite II₁ factor