Geodesic
A criterion for positive completeness in ternary logic
Diskretnyj analiz i issledovanie operacij, Tome 13 (2006) no. 3, pp. 27-39.

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The operator of positive closure is considered on the set $P_k$ of functions of $k$-valued logic. Some positive complete systems of functions are defined. It is proved that every positive complete class of functions from $P_k$ is positive generated by the set of all functions depending on at most $k$ variables. For each $k\geqslant 3$, the three families of positive precomplete classes are defined. It is shown that, for $k=3$, the 10 classes of these families constitute a criterion system. 
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S. S. Marchenkov. A criterion for positive completeness in ternary logic. Diskretnyj analiz i issledovanie operacij, Tome 13 (2006) no. 3, pp. 27-39. http://geodesic.mathdoc.fr/item/DA_2006_13_3_a2/

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