Iterated Kleene computability (Q2639056)

The author continues his earlier investigations [Mat. Sb., Nov. Ser. 101, 21-43 (1976; Zbl 0342.02031); Algebra Logika 12, 3-21 (1973; Zbl 0291.02029)]. He defines enumerated transfinite sequences of oracles of a special type to define a class of ``algorithms'' admitting an infinite search. Each of these oracles is a fixed point of a monotone functional. The author shows that, in general, his oracles are not equivalent to those of \textit{S. C. Kleene} [Trans. Am. Math. Soc. 91, 1-52 (1959; Zbl 0088.012)] while, under some conditions, they are. For better understanding the reader must be familiar with two papers by \textit{E. I. Nikiforova} [Vychisl. Sist. 107, 80-95 (1985; Zbl 0621.03032); Recursive hierarchies, regular by construction (Russian) (1986, unpublished)].