Geodesic
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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{AL_2002_41_2_a3,
     author = {Yu. D. Korolkov},
     title = {Evaluating the {Complexity} of {Index} {Sets} for {Families} of {General} {Recursive} {Functions} in the {Arithmetic} {Hierarchy}},
     journal = {Algebra i logika},
     pages = {155--165},
     publisher = {mathdoc},
     volume = {41},
     number = {2},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2002_41_2_a3/}
}
TY  - JOUR
AU  - Yu. D. Korolkov
TI  - Evaluating the Complexity of Index Sets for Families of General Recursive Functions in the Arithmetic Hierarchy
JO  - Algebra i logika
PY  - 2002
SP  - 155
EP  - 165
VL  - 41
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2002_41_2_a3/
LA  - ru
ID  - AL_2002_41_2_a3
ER  - 
%0 Journal Article
%A Yu. D. Korolkov
%T Evaluating the Complexity of Index Sets for Families of General Recursive Functions in the Arithmetic Hierarchy
%J Algebra i logika
%D 2002
%P 155-165
%V 41
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2002_41_2_a3/
%G ru
%F AL_2002_41_2_a3
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/

[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