  We study two generalizations of the Rudin-Keisler ordering to ultrafilters on
complete Boolean algebras. To highlight the difference between them, we develop
new techniques to construct incomparable ultrafilters in this setting.
Furthermore, we discuss the relation with Tukey reducibility and prove that,
assuming the Continuum Hypothesis, there exist ultrafilters on the Cohen
algebra which are RK-equivalent in the generalized sense but
Tukey-incomparable, in stark contrast with the classical setting.
