Geodesic
On simple bases of $k$-valued logic
Matematičeskie zametki, Tome 5 (1969) no. 4, pp. 471-482.

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The paper derives an asymptotic iterated (two-fold) logarithm of the number of simple bases in $P_k$, as well as the maximal order of the functions prime for each precomplete class in $P_3$. 
@article{MZM_1969_5_4_a10,
     author = {V. B. Alekseev},
     title = {On simple bases of $k$-valued logic},
     journal = {Matemati\v{c}eskie zametki},
     pages = {471--482},
     publisher = {mathdoc},
     volume = {5},
     number = {4},
     year = {1969},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1969_5_4_a10/}
}
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V. B. Alekseev. On simple bases of $k$-valued logic. Matematičeskie zametki, Tome 5 (1969) no. 4, pp. 471-482. http://geodesic.mathdoc.fr/item/MZM_1969_5_4_a10/