  In the setting of modern mathematical logic and model theory, classification
theory has been one of the landmark achievements of the field. Likewise, the
classification of UHF-algebras and AF-algebras were substantial contributions
to the field of operator algebra theory. These seemingly disparate topics of
study in mathematics, model theory and operator algebras, have in recent years
become closely related in many respects. I here attempt to bridge the gap
between these two topics by discussing how operator algebraic classifications
may be understood in terms of model-theoretic classification theory. This
introductory article assumes basic familiarity with model theory and linear
operator, but higher-level concepts are introduced when necessary. The focus of
this introduction is conceptual and informal, and as such, many results are
stated without proof, but relevant sources are cited for completeness. The
reader should take this not as a detailed review, but rather as an overview of
a general narrative thread connecting these two branches of modern mathematics.
