On the relationship between density and weak density in Boolean algebras

Abstract:

Given a homogeneous, complete Boolean algebra $B$, it is shown that ${\text {d}}(B) \leq \min ({2^{ < {\text {wd}}(B)}},\sup \{ {\lambda ^{c(B)}}:\lambda < {\text {wd}}(B)\} )$ in ZFC, where $d(B)$ is the density, ${\text {wd}}(B)$ is the weak density, and $c(B)$ is the cellularity of $B$. A corollary to this result is that $d(B) = {\text {wd}}(B)$ in ZFC+GCH.