The Number of Near-Coherence Classes of Ultrafilters

We prove that the number of near-coherence classes of non-principal ultrafilters on the natural numbers is either finite or 2c. Moreover, in the latter case the Stone-Čech compactification βω of ω contains a closed subset C consisting of 2c pairwise non-nearly-coherent ultrafilters. We obtain some additional information about such closed sets under certain assumptions involving the cardinal characteristics u and d. Applying our main result to the Stone-Čech remainder βR+ −R+ of the half-line R+ = [0,∞) we obtain that the number of composants of βR+ − R+ is either finite or 2 c.