  We answer Blass' question from 1989 of whether the inequality $\gu < \gro$ is
strictly stronger than the filter dichotomy principle affirmatively. We show
that there is a forcing extension in which every non-meagre filter on $\omega$
is ultra by finite-to-one and the semifilter trichotomy does not hold. This
trichotomy says: every semifilter is either meagre or comeagre or ultra by
finite-to-one. The trichotomy is equivalent to the inequality $\gu<\gro$ by
work of Blass and Laflamme. Combinatorics of block sequences is used to
establish forcing notions that preserve suitable properties of block sequences.
