In this article we, given a free ultrafilter p on ω, consider the following classes of ultrafilters: (1) T (p) the set of ultrafilters Rudin-Keisler equivalent to p, (2) S(p) = {q ∈ ω∗ : ∃ f ∈ ω, strictly increasing, such that q = f β(p)}, (3) I (p) the set of strong Rudin-Blass predecessors of p, (4) R(p) the set of ultrafilters equivalent to p in the strong Rudin-Blass order, (5) PRB(p) the s...
