Evasion and prediction III Constant prediction and dominating reals

Abstract

We prove that $b\le 0_2^{const}$ where $b$ is as usual the unbounding number, and $0_2^{const}$ is the constant prediction number, that is, the size of the least family $\Pi$ of functions $\pi$ : such that for each $x\in 2^{\omega }$ there are $\pi \in \Pi$ and $k$ such that for almost all intervals I of length $k$, one has $\pi (x\uparrow i)=x\left(i\right)$ for some $i\in I$. This answers a question of Kamo. We also include some related results.