Model theory of operator systems and C∗-algebras
Thomas Sinclair · 2023
We survey the model theory of operator systems and C∗-algebras. We begin with a brief introduction to operator system theory. We then describe the languages and model-theoretic axiomatizations of the classes of operator systems and C∗-algebras, including discussions of ultraproducts and definability in both contexts. Finally, we show how various well-studied approximation properties of operator systems and C∗-algebras may be viewed from the perspective of continuous model theory. Along the way new approaches to several results in the literature are developed.