There are no $Q$-Points in Laver's Model for the Borel Conjecture
Arnold W. Miller
Proceedings of the American Mathematical Society, Vol. 78, No. 1. (Jan., 1980), pp. 103-106.
AbstractIt is shown that it is consistent with ZFC that no nonprincipal ultrafilter on $\omega$ is a $Q$-point (also called a rare ultrafilter).