Abstract

We study ω‐categorical weakly o‐minimal expansions of Boolean lattices. We show that a structure ???? = (A,≤, ℐ) expanding a Boolean lattice (A,≤) by a finite sequence I of ideals of A closed under the usual Heyting algebra operations is weakly o‐minimal if and only if it is ω‐categorical, and hence if and only if A/I has only finitely many atoms for every I ∈ ℐ. We propose other related examples of weakly o‐minimal ω‐categorical models in this framework, and we examine the internal structure of these models.