Sam Kim, Department of Pure Mathematics, University of Waterloo
"Some logical aspects of hyperrigidity of operator systems"
Hyperrigidity and the C*-envelope of an operator system provide an interesting interplay between operator systems and the theory of C*-algebras. In this talk we look at these properties from two contrasting viewpoints. On the one hand, we show that both hyperrigidity and C*-envelopes reflect to separable substructures in the sense of Farah, showing that we can get many examples of separable hyperrigid operator systems from their non-separable counterparts. On the other hand, we show that hyperrigidity and C*-envelopes are badly behaved with respect to a logical relation called elementary equivalence. In particular, we find a sequence of hyperrigid operator systems whose ultraproduct is not hyperrigid and we find operator systems which are elementarily equivalent but whose C*-envelopes are not elementarily equivalent.
MC 5417