Cardinal invariants associated with predictors II

Abstract

We call a function from to $\omega$ a predictor. A function $f\in {\omega }^{\omega }$ is said to be constantly predicted by a predictor $\pi$, if there is an such that . Let ${\theta }_{\omega }$ denote the smallest size of a set $\Phi$ of predictors such that every $f\in {\omega }^{\omega }$ can be constantly predicted by some predictor in $\Phi$. In [7], we showed that ${\theta }_{\omega }$ may be greater than $cof\left(\mathcal{N}\right)$. In the present paper, we will prove that ${\theta }_{\omega }$ may be smaller than $d$.