Cardinal invariants associated with predictors II

Abstract

We call a function from omega^<omega to ω a predictor. A function f∈omega^omega is said to be constantly predicted by a predictor π, if there is an n<omega such that ∀ i<omega∃ j∈[i, i+n) (f(j)=π(f↑ j)). Let θ_omega denote the smallest size of a set ¶hi of predictors such that every f∈omega^omega can be constantly predicted by some predictor in ¶hi. In [{7}], we showed that θ_omega may be greater than cof(\mathscr{N}). In the present paper, we will prove that θ_omega may be smaller than \bm{d}.