Baldwin-Saxl condition

This article defines a property of a group (possibly with additional operations and structure) as viewed in logic/model theory

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.