  We introduce Gowers--Matet forcing with a finite sequence of pairwise
non-isomorphic Ramsey ultrafilters over $\omega$, and with this forcing we
settle the long-standing problem of the spectrum of numbers near-coherence
classes. We prove that for any finite $n \geq 1$, there is a forcing extension
with exactly $n$ near-coherence classes of ultrafilters.
  For evaluating the new forcing, we prove a strengthening of Gowers's theorem
on colourings of ${\rm Fin}_k$.
