A consistency result on thin-tall superatomic Boolean algebras

Abstract:

We prove that if $[unk]$ is an infinite cardinal with ${[unk]^{ < [unk]}} = [unk]$, then there is a cardinal-preserving notion of forcing that forces the existence of a $[unk]$-thin-tall superatomic Boolean algebra. Consistency for specific $[unk]$, like ${\omega _1}$, then follows as a corollary.