Constructing Boolean algebras for cardinal invariants. (Q1771845)

At first, the author solves two problems of J. D. Monk: 1. He proves in ZFC that for some superatomic Boolean algebra \(B\) there holds \(\text{Aut} (B) < \text{End} (B)\). 2. He constructs in ZFC a superatomic Boolean algebra \(B\) such that \(\text{Aut} (B) < | B| \). Then he deals with entangled sequences of linear orders and he constructs Boolean algebras with spread not obtained under ZFC and in which GCH is violated strongly enough, even just for regular cardinals.