Elementary class
In model theory, a branch of mathematical logic, an elementary class (or axiomatizable class) is a class consisting of all structures satisfying a fixed first-order theory. == Definition == A 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.