Ultrafilters on $\omega$
                      Christopher Barney 
Abstract.
We study of filters and ultrafilters on $\omega$ from the prospective
of cardinal invariants of the continuum, focusing on the existence and
generic existence of certain special ultrafilters. We show that
the general existence of Q-points is independent of the cardinal
invariants that previously partially categorized it. We sharpen
another side of the picture on generic existence with the introduction
of the ${\mathcal K}_\sigma$ ultrafilter, getting a new equality of
cardinal invariants in the process. We also answer an open question of
J\"org Brendle by separating two classes of ultrafilters previously
unseparated.