Geodesic
On two intervals in the lattice of partial ultraclones of rank~$2$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 1, pp. 262-274

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In article the intervals in the lattice of partial ultraclones of rank $2$ are considered. The well-known classes of all monotone $M$ and all self-dual $S$ Boolean functions are partial ultraclones of rank $2$. We proved that each of the intervals $\Im (M, M_2)$ and $\Im (S, M_2)$, where $M_2$ is complete partial ultraclone of rank $2$, is finite.
Keywords: multifunction, Boolean function, monotone function, self-dual function, closed set, clone, partial ultraclone, lattice, interval of lattice.
Mots-clés : superposition 
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     author = {S. A. Badmaev and A. E. Dugarov and I. V. Fomina and I. K. Sharankhaev},
     title = {On two intervals in the lattice of partial ultraclones of rank~$2$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {262--274},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2023_20_1_a8/}
}
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S. A. Badmaev; A. E. Dugarov; I. V. Fomina; I. K. Sharankhaev. On two intervals in the lattice of partial ultraclones of rank~$2$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 1, pp. 262-274. http://geodesic.mathdoc.fr/item/SEMR_2023_20_1_a8/