Geodesic
Examples of $\alpha$-complete systems of $k$-valued logic for $k=3,4$
Diskretnaya Matematika, Tome 18 (2006) no. 4, pp. 45-55 
A. L. Shabunin. Examples of $\alpha$-complete systems of $k$-valued logic for $k=3,4$. Diskretnaya Matematika, Tome 18 (2006) no. 4, pp. 45-55. http://geodesic.mathdoc.fr/item/DM_2006_18_4_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In the paper, we prove the $\alpha$-completeness of finite systems of function of $k$-valued logic for $k=3,4$ containing all permutations of the symmetric group $S_k$ on the set $E_k=\{0,1,\dots,k-1\}$, the operation of addition modulo $k$, and $k$ certain binary operation. This result is extended to some other systems of functions which are obtained by replacing the operation of addition by some quasi-group operation.

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