The character spectrum of beta(N)

TL;DR

This paper investigates the possible structures of the set of characters of ultrafilters on omega, demonstrating that these sets can be highly non-convex and contain many gaps, revealing complex behaviors.

Contribution

It establishes the consistency of ultrafilter character sets being non-convex and having gaps, advancing understanding of ultrafilter spectra on omega.

Findings

The set of regular cardinals as ultrafilter characters can be non-convex.

Ultrafilter character sets can have many gaps.

The paper explores pi-characters of ultrafilters on omega.

Abstract

We show the consistency of: the set of regular cardinals which are the character of some ultrafilter on omega can be quite chaotic, in particular not only can be not convex but can have many gaps. We also deal with the set of pi-characters of ultrafilters on omega.