Distributivity of the algebra of regular open subsets of βR∖R

We compare the structure of the algebras P(ω)/fin and Aω/Fin, where A denotes the algebra of clopen subsets of the Cantor set. We show that the distributivity number of the algebra Aω/Fin is bounded by the distributivity number of the algebra P(ω)/fin and by the additivity of the meager ideal on the reals. As a corollary we obtain a result of A. Dow, who showed that in the iterated Mathias model the spaces βω∖ω and βR∖R are not co-absolute. We also show that under the assumption t=h the spaces βω∖ω and βR∖R are co-absolute, improving on a result of E. van Douwen.