On skew ultralimits and their applications in ultrafilter theory

Abstract

We define a special version of the ultralimit, called the skewed ultralimit. Using this tool, we show that the set of ultrafilter types in the $C$-equivalence class of a Ramsey ultrafilter $\mathfrak{u}\in \beta \omega$ with the Rudin-Keisler order is isomorphic to the ultrapower of $(\omega ,\le )$.