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1 results

WEAK DISTRIBUTIVITY IMPLYING DISTRIBUTIVITY
DAN HATHAWAY
Journal:

The Journal of Symbolic Logic / Volume 81 / Issue 2 / June 2016

Published online by Cambridge University Press:

29 June 2016, pp. 711-717

Print publication:

June 2016
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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.