3 problems

Countability conjecture. The minor equivalence relation on clones on finite domains has only countably many classes.

The three-submaximal-clones conjecture. The poset $\mathfrak P_3$ has exactly three submaximal elements, namely the minor-equivalence classes of $\mathcal C_2$, $\mathcal C_3$, and…

Three-element reduction conjecture. Every clone on three elements that does not admit a minor-preserving map from ${\mathbf I}$ has a minor-preserving map to one of the following t…