Historic forcing for Depth
We show that, consistently, for some regular cardinals θ <λ, there exists a Boolean algebra 𝔹 such that |𝔹| = λ⁺ and for every subalgebra 𝔹'⊆ 𝔹 of size λ⁺ we have Depth(𝔹') = θ.
Homeomorphisms of products of Boolean separable spaces
Horizontal sums of basic algebras
The variety of basic algebras is closed under formation of horizontal sums. We characterize when a given basic algebra is a horizontal sum of chains, MV-algebras or Boolean algebras.