Depth, π-character, and tightness in superatomic Boolean algebras

Theorem A. There is a superatomic Boolean algebra B with size and π-character equal to ω1 and countable depth. Theorem B. If B is a superatomic Boolean algebra with π-character greater than ω1, then the π-character and depth of B are the same. Theorem C. I κ → (κ)2<ω, then every superatomic Boolean algebra with tightness at least κ+ has depth at least κ.