Elementary class - Wikipedia
https://en.wikipedia.org/wiki/Elementary_classA class K of structures of a signature σ is called an elementary class if there is a first-order theory T of signature σ, such that K consists of all models of T, i.e., of all σ-structures that satisfy T. If T can be chosen as a theory consisting of a single first-order sentence, then K is called a basic elementary class. More generally, K is a pseudo-elementary classif there is a first-order theory T of a signature tha…