Geodesic
On some intervals in the lattice of ultraclones of rank~$2$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1210-1218

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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.
Keywords: hyperfunction, Boolean function, monotone function, self-dual function, linear function, closed set, clone, ultraclone, lattice, interval of lattice.
Mots-clés : superposition 
@article{SEMR_2021_18_2_a8,
     author = {S. A. Badmaev and A. E. Dugarov and I. V. Fomina and I. K. Sharankhaev},
     title = {On some intervals in the lattice of ultraclones of rank~$2$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1210--1218},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a8/}
}
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S. A. Badmaev; A. E. Dugarov; I. V. Fomina; I. K. Sharankhaev. On some intervals in the lattice of ultraclones of rank~$2$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1210-1218. http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a8/