Geodesic
Conditions for the $\alpha$-completeness of systems of many-valued logic functions
Diskretnaya Matematika, Tome 4 (1992) no. 4, pp. 117-130 
A. L. Chernyshov. Conditions for the $\alpha$-completeness of systems of many-valued logic functions. Diskretnaya Matematika, Tome 4 (1992) no. 4, pp. 117-130. http://geodesic.mathdoc.fr/item/DM_1992_4_4_a10/
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     author = {A. L. Chernyshov},
     title = {Conditions for the $\alpha$-completeness of systems of many-valued logic functions},
     journal = {Diskretnaya Matematika},
     pages = {117--130},
     year = {1992},
     volume = {4},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1992_4_4_a10/}
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Conditions of $\alpha$-completeness are presented for systems of functions of $k$-valued logic consisting of functions whose one-place subfunctions obtained by arbitrarily fixing all variables except one, are substitutions. For $k\ne2,3,4$, $\alpha$-complete systems of two binary operations with right cancellation are constructed, and for $k=2$, the nonexistence of finite $\alpha$-complete systems is proved.