Weak cylindric set algebras and weak subdirect indecomposability

Abstract

AbstractIn this note we prove that the abstract property “weakly subdirectly indecomposable” does not characterize the class IWsα of weak cylindric set algebras. However, we give another (similar) abstract property characterizing IWsα. The original property does characterize the directed unions of members of IWsα iff α is countable. Free algebras will be shown to satisfy the original property.