This is an announcement for the paper "Model-theoretic aspects of the Gurarij operator space" by Isaac Goldbring and Martino Lupini.

Abstract: We show that the theory of the Gurarij operator space is the model-completion of the theory of operator spaces, it has a unique separable $1$-exact model, continuum many separable models, and no prime model. We also establish the corresponding facts for the Gurarij operator system. The proofs involve establishing that the theories of the Fra"iss'{e} limits of the classes of finite-dimensional $M_q$-spaces and $M_q$-systems are separably categorical and have quantifier-elimination. We conclude the paper by showing that no existentially closed operator system can be completely order isomorphic to a C$^*$ algebra.

Archive classification: math.LO math.FA math.OA

Remarks: 21 pages

Submitted from: isaac@math.uic.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1501.04332

or

http://arXiv.org/abs/1501.04332