Abstract

A free ultrafilter $\mathcal{U}$ on $\omega$ is called a $T$-point if, for every countable group $G$ of permutations of $\omega$, there exists $U\in\mathcal{U}$ such that, for each $g\in G$, the set $\{x\in U:gx\ne x, gx\in U\}$ is finite. We show that each $P$-point and each $Q$-point in $\omega^*$ is a $T$-point, and, under CH, construct a $T$-point, which is neither a $P$-point, nor a $Q$-point. A question whether $T$-points exist in ZFC is open