Forcing and stable ordered-union ultrafilters

Abstract

We investigate the effect of a variant of Matet forcing on ultrafilters in the ground model and give a characterization of those $P$–points that survive such forcing, answering a question left open by Blass. We investigate the question of when this variant of Matet forcing can be used to diagonalize small filters without destroying $P$–points in the ground model. We also deal with the question of generic existence of stable ordered–union ultrafilters.