On the Mitchell and Rudin-Keisler orderings of ultrafilters (Q1110507)

Let \(\triangleleft\) be the Mitchell order and \(\leq_{RK}\) be Rudin- Keisler order of ultrafilters. Restricting his attention to \(\kappa\)- complete ultrafilters on \(\kappa\) for various \(\kappa\) the author compares the consistency strength of ``there exists an increasing \(\triangleleft\)-sequence of length \(\alpha\) '' and ``there exists an increasing \(\leq_{RK}\)-sequence of length \(\beta\) '' for various \(\alpha\) and \(\beta\).