WEAK DISTRIBUTIVITY IMPLYING DISTRIBUTIVITY

Abstract Let $B$ be a complete Boolean algebra. We show that if λ is an infinite cardinal and $B$ is weakly (λω, ω)-distributive, then $B$ is (λ, 2)-distributive. Using a similar argument, we show that if κ is a weakly compact cardinal such that $B$ is weakly (2κ, κ)-distributive and $B$ is (α, 2)-distributive for each α < κ, then $B$ is (κ, 2)-distributive.