In this paper we use the version CPAprismgame 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 \omega1-OK point.
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Last modified July 26, 2004.