Evaluating the Complexity of Index Sets for Families of General Recursive Functions in the Arithmetic Hierarchy
Algebra i logika, Tome 41 (2002) no. 2, pp. 155-165

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The complexity of index sets of families of general recursive functions is evaluated in the Kleene – Mostowski arithmetic hierarchy.
Keywords: general recursive function, computable family of general recursive functions, discrete family of general recursive functions, effectively discrete family of general recursive functions.
Yu. D. Korolkov. Evaluating the Complexity of Index Sets for Families of General Recursive Functions in the Arithmetic Hierarchy. Algebra i logika, Tome 41 (2002) no. 2, pp. 155-165. http://geodesic.mathdoc.fr/item/AL_2002_41_2_a3/
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[1] Yu. L. Ershov, Teoriya numeratsii, Nauka, M., 1977 | MR

[2] Yu. L. Ershov, Theory of numberings, preprint No 18, NII MIOO NGU, Novosibirsk, 1996 | MR

[3] V. L. Selivanov, “Tonkie ierarkhii arifmeticheskikh mnozhestv i opredelimye indeksnye mnozhestva”, Matematicheskaya logika i algoritmicheskie voprosy, Tr. In-ta matem. SO AN SSSR, 12, Nauka, Novosibirsk, 1989, 165–185 | MR

[4] A. H. Lachlan, “On the indexing of classes of recursively enumerable sets”, J. Symb. Log., 31:1 (1966), 10–22 | DOI | MR | Zbl

[5] H. G. Rice, “On completely recusive enumerable classes and their key arrays”, J. Symb. Log., 21:3 (1956), 304–308 | DOI | MR | Zbl

[6] Yu. L. Ershov, “Numeratsii semeistv obscherekursivnykh funktsii”, Sib. matem. zh., 8:5 (1967), 1015–1025

[7] A. I. Maltsev, Algoritmy i rekursivnye funktsii, Nauka, M., 1965 | MR

[8] Yu. D. Korolkov, “O svodimosti indeksnykh mnozhestv semeistv obscherekursivnykh funktsii”, Sib. matem. zh., 23:1 (1982), 190–193 | MR

[9] Yu. D. Korolkov, Vychislimye semeistva obscherekursivnykh funktsii, Irkutskii un-t, Irkutsk, 1992