Аннотации:
The class K of algebraic systems of signature σ is called a formula-definable class if there exists an algebraic
system A of signature σ such that for any algebraic system B of signature σ it is B ∈ K if and only
if T h(B) · T h(A) = T h(A). The paper shows that the formula-definable class of algebraic systems is
idempotently formula-definable and is an axiomatizable class of algebraic systems. Any variety of algebraic
systems is an idempotently formula-definite class. If the class K of all existentially closed algebraic systems
of a theory T is formula-definable, then a theory of the class K is a model companion of the theory T. Also,
in the paper the examples of some theories on the properties of formula-definability, pseudofiniteness and
smoothly approximability of their model companion were discussed.
