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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, ₀) -selective ultrafilter, but no nowhere dense ultrafilters is produced. It is thus proved that the existence of (2, ₀) -selective ultrafilters does not imply the existence of nowhere dense ultrafilters.
Raghavan et al. (Thu,) studied this question.