On an infinite set , 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 together with one nonisolated point whose ultrafilter contains all cofinite sets. For countably infinite 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.

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  1. Boolean algebra
  2. Distributive lattice
  3. Lattice
  4. Intuitionistic propositional logic
  5. Propositional logic
  6. Mathematical logic
  7. Foundations of mathematics
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