Computably categorical Boolean algebras enriched by ideals and atoms

We describe computably categorical Boolean algebras whose language is enriched by one-place predicates that distinguish a finite set of ideals and atoms with respect to some ideals in this set.

► We investigate Boolean algebras in an enriched language.
► The language is enriched by a finite number of ideals and sets of atoms w.r.t. ideals.
► We algebraically describe computably categorical structures of this form.