Adding ultrafilters to Shelah's model for no nowhere dense ultrafilters

Abstract

We exhibit a forcing for producing a model with no nowhere dense ultrafilters that satisfies the full Sacks Property. By interleaving this forcing with other forcing notions, a model containing a $(2,{\aleph }_0)$-selective ultrafilter, but no nowhere dense ultrafilters is produced. It is thus proved that the existence of $(2,{\aleph }_0)$-selective ultrafilters does not imply the existence of nowhere dense ultrafilters.

17 Pages, Submitted