Constant prediction and evasion number, I: Generalization and variants

Using the concept of constant evasion to different sorts of suitable binary relations, we establish many cardinal invariants derived from the established cardinal invariants $\mathfrak{e}^\mathrm{const}_{n}$ and $\mathfrak{v}^\mathrm{const}_{n}$, called the constant evasion number and the constant prediction number. We formulate several limits and consistency results pertaining to them.