Stable ordered-union versus selective ultrafilters

TL;DR

This paper demonstrates the consistency of having multiple non-isomorphic selective ultrafilters while no stable ordered-union ultrafilters exist, addressing a question posed by Blass in 1987.

Contribution

It provides the first consistency result distinguishing between selective ultrafilters and stable ordered-union ultrafilters.

Findings

Existence of at least two non-isomorphic selective ultrafilters

Non-existence of stable ordered-union ultrafilters under certain conditions

Answers a longstanding open question from Blass (1987)

Abstract

It will be shown to be consistent that there are at least two non-isomorphic selective ultrafilters, but no stable ordered-union ultrafilters. This answers a question of Blass from his 1987 paper which introduced the concept of a stable ordered-union ultrafilter.