Geodesic
Iterated Kleene computability and the superjump
Sbornik. Mathematics, Tome 30 (1976) no. 1, pp. 17-37 
N. V. Beljakin. Iterated Kleene computability and the superjump. Sbornik. Mathematics, Tome 30 (1976) no. 1, pp. 17-37. http://geodesic.mathdoc.fr/item/SM_1976_30_1_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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. Bibliography: 10 titles.

[1] N. V. Belyakin, “Obobschennye vychisleniya i arifmetika vtoroi stupeni”, Algebra i logika, 9:4 (1970), 375–405 | Zbl

[2] N. V. Belyakin, “Obobschennye vychisleniya”, Trudy matem. instituta im. V. A. Steklova, CXXXIII (1973), 59–64

[3] N. V. Belyakin, “Ob odnom klasse rekursivnykh ierarkhii”, Algebra i logika, 12:1 (1973), 3–21 | MR | Zbl

[4] N. V. Belyakin, “Obobschennye vychisleniya nad regulyarnymi numeratsiyami”, Algebra i logika, 12:6 (1973), 623–643 | MR | Zbl

[5] S. C. Kleene, “Recursive functionals and quantifiers of finite types”, Trans. Amer. Math. Soc., 91 (1959), 1–52 | DOI | MR | Zbl

[6] S. C. Kleene, “Turing-machine computable functionals of finite types”, Logic, methodology and philosophy of science, Proc. of the 1960 International congress, Stanford University Press, 1962, 38–45 | MR

[7] P. Aczel, P. A. Hinman, “Recursion in the superjump”, Generalized Recursion Theory, North Holland, 1974 | MR

[8] Kh. Rodzhers, Teoriya rekursivnykh funktsii i effektivnaya vychislimost, izd-vo «Mir», Moskva, 1972 | MR

[9] S. K. Klini, Vvedenie v metamatematiku, IL, Moskva, 1957

[10] W. Richter, “Recursively Mahlo ordinals and inductive definitions”, Proc. Summer School and Colloquium in Math. Logic (Manchester, August 1969), North Holland, 1971, 273–288 | MR