On simple bases of k-valued logic

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 P₃.Translated from Matematicheskie Zametki, Vol. 5, No. 4, pp. 471–482, April, 1969.The author wishes to take this opportunity to express his gratitude to S. V. Yablonskii under whose direction this paper was written.