Weak Distributivity Implying Distributivity

Abstract

Let $\mathbb{B}$ be a complete Boolean algebra. We show, as an application of a previous result of the author, that if $\lambda$ is an infinite cardinal and $\mathbb{B}$ is weakly $({\lambda }^{\omega },\omega )$-distributive, then $\mathbb{B}$ is $(\lambda ,2)$-distributive. Using a parallel result, we show that if $\kappa$ is a weakly compact cardinal such that $\mathbb{B}$ is weakly $(2^{\kappa },\kappa )$-distributive and $\mathbb{B}$ is $(\alpha ,2)$-distributive for each $\alpha <\kappa$, then $\mathbb{B}$ is $(\kappa ,2)$-distributive.

arXiv comment12 pages

References in corpus (1)

• A Lower Bound for Generalized Dominating Numbers