Weak cylindric set algebras and weak subdirect indecomposability

Journal of Symbolic Logic 55 (2):577-588 (1990)
Abstract
In this note we prove that the abstract property "weakly subdirectly indecomposable" does not characterize the class IWs α of weak cylindric set algebras. However, we give another (similar) abstract property characterizing IWs α . The original property does characterize the directed unions of members of $\mathrm{IWs}_alpha \operatorname{iff} \alpha$ is countable. Free algebras will be shown to satisfy the original property
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