= Finite-cofinite Boolean algebra
On an <infinite set> $D$, take its finite and cofinite <subsets> with ordinary <union>, <intersection> and complement. <Singletons> are its <atom of a Boolean algebra>[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 <atom of a Boolean algebra>[atoms], not the uncountable full <power set>. It describes two-vector definability over a countably infinite <field>: dependent directions are isolated <atom of a Boolean algebra>[atoms] and the independent-pair type is the additional nonisolated point.
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