Distributivity of the algebra of regular open subsets of

We compare the structure of the algebras P ( ω ) / fin and A ω / Fin , where A denotes the algebra of clopen subsets of the Cantor set. We show that the distributivity number of the algebra A ω / 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 β ω ∖ ω and β R ∖ R are not co-absolute. We also show that under the assumption t = h the spaces β ω ∖ ω and β R ∖ R are co-absolute, improving on a result of E. van Douwen.