Evasion and prediction III Constant prediction and dominating reals

Source abstract

We prove that b≤02const where b is as usual the unbounding number, and 02const is the constant prediction number, that is, the size of the least family Π of functions π : 2<ω→2 such that for each x∈2ω 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.