Iterated Kleene computability and the superjump

Recursive hierarchies obtained by iterating the well-known version, developed by S. C. Kleene, of recursiveness relative to objects of type $\leqslant2$ are studied in the article. Iteration is carried out over ordinal indexings which, in a definite sense, are effectively constructed. An estimate is given for classes corresponding to critical points of the hierarchies under consideration.
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