On skew ultralimits and their applications in ultrafilter theory

TL;DR

This paper introduces the skewed ultralimit, a novel ultralimit variant, and demonstrates its application in showing the isomorphism between ultrafilter types in a Ramsey ultrafilter's class and an ultrapower of the natural numbers.

Contribution

It defines the skewed ultralimit and applies it to establish a new isomorphism result in ultrafilter theory, linking ultrafilter types to ultrapowers.

Findings

The set of ultrafilter types in a Ramsey ultrafilter's class is isomorphic to an ultrapower of (ω, ≤).

The skewed ultralimit provides a new tool for ultrafilter analysis.

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 $(\omega, \leq)$.