Minimal coverings of maximal partial clones

A partial function f on a κ-element set Eκ is a partial Sheffer function if every partial function on Eκ is definable in terms of f. Since this holds if and only if f belongs to no maximal partial clone on Eκ, a characterization of partial Sheffer functions reduces to finding families of minimal coverings of maximal partial clones on Eκ. We show that for each κ ≥ 3 there exists a unique minimal covering

Uniqueness of minimal coverings of maximal partial clones

A partial function f on a k-element set Ek is a partial Sheffer function if every partial function on Ek is definable in terms of f. Since this holds if and only if f belongs to no maximal partial clone on Ek, a characterization of partial Sheffer functions reduces to finding families of minimal coverings of maximal partial clones on Ek. We show that for each k ≥ 2, there exists a unique minimal covering

The minimal covering of maximal partial clones in 4-valued logic

A partial function f on a κ-element set Eκ is a partial Sheffer function if every partial function on Eκ is definable in terms of f. Since this holds if and only if f belongs to no maximal partial clone on Eκ, a characterization of partial Sheffer functions reduces to finding families of minimal coverings of maximal partial clones on Eκ. It is shown that