Baldwin-Saxl condition

Definition
A group (possibly with additional structure and relations) is said to satisfy the Baldwin-Saxl condition if given any formula $$f(x,\overline{y})$$ in the theory of the group, there is a natural number $$n$$ such that the intersection of an arbitrary family of subgroups defined by $$f(x,\overline{a_i})$$ is equal to an intersection of $$n$$ of them. This means that the groups that are intersections of any family ,finite or infinite, of subgroups defined by the formula $$f(x,\overline{a_i})$$ form a uniformly definable family of subgroups.