On some intervals in the lattice of ultraclones of rank 2

Abstract

In article the intervals in the lattice of ultraclones of rank 2 are considered. The well-known classes of all monotone $M$, all self-dual $S$ and all linear $L$ Boolean functions are ultraclones of rank 2. We proved that each of the intervals $\Im (M, H_2)$, $\Im (S, H_2)$, $\Im(L, H_2)$, where $H_2$ is complete ultraclone of rank 2, contains exactly 4 elements.