Categorical Abstract Algebraic Logic: Operators on Classes of Structure Systems

The study of structure systems, an abstraction of the concept of firstorder structures, is continued. Structure systems have algebraic systems, rather than universal algebras, as their algebraic reducts. Moreover, their relational component consists of a collection of relation systems on the underlying functors, rather than simply a system of relations on a single set. A variety of operators on classes of structure systems are introduced and studied, taking after similar work of Elgueta in the context of the model theory of equality-free first-order logic. Both Elgueta’s and the present work are inspired by considerations arising in the study of the process of algebraization in abstract algebraic logic. The ways that these various class operators interact, when composed with one-another, are at the focus of current investigations.