Depth, \(\pi\)-character, and tightness in superatomic Boolean algebras (Q675241)

It is shown that \(\pi\)-character = depth in any superatomic Boolean algebra \(B\) provided that \(\pi\)-character of \(B\) is greater than \(\omega_1\). On the other hand, an example is given of a superatomic Boolean algebra with countable depth and \(\pi\)-character equal to \(\omega\). The difference between depth and tightness in superatomic Boolean algebras is also considered.