Between p-points and nowhere dense ultrafilters

We discuss the problem of existence and that of generic existence for various classes of ultrafilters onω. For example, we prove it is consistent that there are nowhere dense ultrafilters while there are no measure zero ultrafilters, and that there are measure zero ultrafilters while there are no P-points. We also prove that every filter base of size <c can be extended to a nowhere dense ultrafilter iff cof ( % MathType!End!2!1!)=c, and that every filter base of size <c can be extended to an ordinal ultrafilter iff ∂=c. Along the way we get a few new results on cardinal invariants of the continuum.