On the model theory of C* algebras


Ultrapowers and reduced products play a central role in the Elliott classification program for separable (nuclear, etc.) C*-algebras. Although an ultrapower of a separable C*-algebra A is quite different from the reduced product $\ell_\infty(A)/c_0(A)$, these massive algebras are interchangeable in many (but not quite all) concrete applications. I will present a theorem that attempts to give an abstract explanation of this phenomenon. This preliminary result applies to some other axiomatizable categories, and its proof does not use any of the nontrivial theory of C*-algebras.

No previous knowledge of C*-algebras is required; they appear primarily as a motivation. This is preliminary part of a joint work with Christopher Schafhauser.