 Finite-cofinite Boolean algebra

On an infinite set $D$, take its finite and cofinite subsets with ordinary union, intersection and complement. Singletons are its atoms. Its Stone space consists of the isolated points of $D$ together with one nonisolated point whose ultrafilter contains all cofinite sets. For countably infinite $D$ this is a countable Boolean algebra with countably many atoms, not the uncountable full power set. It describes two-vector definability over a countably infinite field: dependent directions are isolated atoms and the independent-pair type is the additional nonisolated point.