This paper continues the paper of N. Kh. Kasymov and the author [Vychisl. Sist. 116, 3-15 (1986; Zbl 0646.03042)]. The author states some results for the equivalence relation generated by a recursively enumerable set \(\alpha\) to be finitely generated from a finite number of constants by a finite number of recursive functions. There are no proofs in the paper.