Shelah's model for no nowhere dense ultrafilters and (m,n)-selectivity
The talk will be mostly expository, providing a slightly different perspective on Shelah's model in which there are nowhere dense ultrafilters. It will be shown how a slight variant allows the weak Sacks property to be replaced by the Sacks property.
One might hope that this model is a strong candidate to destroy various properties enjoyed by P-points, but this often fails to be the case. One such example is the notion of (n,m)-selectivity introduced by Bartosova and Zucker. It will be shown that this notion of selectivity is not strong enough to imply the existence of nowhere dense ultrafilters.
The new results in this talk are joint work with Dilip Raghavan.