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WEAK DISTRIBUTIVITY IMPLYING DISTRIBUTIVITY

Published online by Cambridge University Press:  29 June 2016

DAN HATHAWAY*
Affiliation:
MATHEMATICS DEPARTMENTUNIVERSITY OF DENVERDENVER, CO80208, USAE-mail:daniel.hathaway@du.edu

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.

Type
Articles
Copyright
Copyright © The Association for Symbolic Logic 2016 

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References

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