In this paper we use the version
CPA_{prism}^{game} of
the Covering Property Axiom, which has been formulated by Ciesielski
and Pawlikowski and holds in the iterated perfect set model,
to study the relations between different kinds of ultrafilters on \omega
and **Q**.
In particular, we will give a full account for the logical relations
between the properties of being a selective ultrafilter, a P-point,
a Q-point, and an \omega_{1}-OK point.

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**Last modified July 26, 2004.**