Adding the constant evasion and constant prediction numbers to Cichoń's maximum

Abstract

Let $\mathfrak{e}^\mathsf{const}_2$ be the constant evasion number, that is, the size of the least family $F\subseteq{}^ω2$ of reals such that for each predictor $π\colon {}^{<ω}2\to 2$ there is $x\in F$ which is not constantly predicted by $π$; and let $\mathfrak{v}_2^\mathsf{const}$ be the constant prediction number, that is, the size of the least family $Π_2$ of functions $π\colon {}^{<ω}2\to 2$ such that for each $x\in{}^ω2$ there is $π\inΠ_2$ that predicts constantly $x$. In this work, we show that the constant evasion number $\mathfrak{e}_2^{\mathrm{cons}}$ and the constant prediction number $\mathfrak{v}_2^\mathsf{const}$ can be added to Cichoń's maximum with distinct values.