Ordinal ultrafilters versus P-hierarchy

TL;DR

This paper explores the relationship between ordinal ultrafilters and the P-hierarchy, focusing on class characterization, existence, and order relations within the hierarchy.

Contribution

It advances the understanding of the P-hierarchy by characterizing classes of finite index and analyzing their Rudin-Keisler-order relations.

Findings

Characterization of classes of finite index in the P-hierarchy

Existence and generic existence results for certain ultrafilters

Analysis of Rudin-Keisler-order among classes

Abstract

An earlier paper, entitled "P-hierarchy on $\beta\omega$", investigated the relations between ordinal ultrafilters and the so-called P-hierarchy. This study is continued in the present paper and focuses on the aspects of characterization of classes of finite index, existence, generic existence and the Rudin-Keisler-order.