Semilattices of Definable Subalgebras

In issues bearing on the structure of universal algebras $\mathcal A$, derived structures, such as automorphism groups $\operatorname{Aut}\mathcal A$, subalgebra lattices $\operatorname{Sub}\mathcal A$, congruence lattices $\operatorname{Con}\mathcal A$, etc., play an important part. On the other hand, in studying universal algebras by the means of model theory, of crucial importance is the question asking which elements of the derived structures under examination are expressible by one or other formulas in the elementary language. Problems concerning the interrelationship of algebras and their derived structures are treated for subalgebras of universal algebras.