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 ${\mathfrak{e}}_n^{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}}$ and ${\mathfrak{v}}_n^{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}}$, called the constant evasion number and the constant prediction number. We formulate several limits and consistency results pertaining to them.