Evasion and prediction III

Constant prediction and dominating reals

Abstract

We prove that \mathfrak{b}≤ \mathfrak{v}₂^const where \mathfrak{b} is as usual the unbounding number, and \mathfrak{v}₂^const is the constant prediction number, that is, the size of the least family Π of functions π:2^<omega→ 2 such that for each x∈ 2^omega there are π∈Π and k such that for almost all intervals I of length k, one has π(x↑ i)=x(i) for some i∈ I. This answers a question of Kamo. We also include some related results.