A forcing construction of thin-tall Boolean algebras

Abstract

It was proved by Juhász and Weiss that for every ordinal α with ${0 < α < ω_2}$ there is a superatomic Boolean algebra of height α and width ω. We prove that if κ is an infinite cardinal such that $κ^{< κ} = κ$ and α is an ordinal such that $0 < α < κ^{++