4 problems

Nagy–Sergioli's solvability conjecture. Every finite BCK-algebra is solvable.

The commuting-degree realization conjecture. Every value in $\mathcal{CD}(n)$ is the commuting degree of some BCK-algebra of order $n$, for every $n\geq 3$.

Attainability conjecture for double negation degrees. For each $n\geq 3$, every possible double negation degree is attained by some bounded BCK-algebra. Consequently, every rationa…

The variety of commutative BCK-algebras is denoted by $\mathtt{cBCK}$, and a variety is dualisable when it admits a natural duality of the relevant algebraic and topological catego…