Geodesic
Relationships between different forms of relative computability of functions
Sbornik. Mathematics, Tome 35 (1979) no. 3, pp. 425-436 
E. A. Polyakov; M. G. Rozinas. Relationships between different forms of relative computability of functions. Sbornik. Mathematics, Tome 35 (1979) no. 3, pp. 425-436. http://geodesic.mathdoc.fr/item/SM_1979_35_3_a6/
@article{SM_1979_35_3_a6,
     author = {E. A. Polyakov and M. G. Rozinas},
     title = {Relationships between different forms of relative computability of functions},
     journal = {Sbornik. Mathematics},
     pages = {425--436},
     year = {1979},
     volume = {35},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1979_35_3_a6/}
}
TY  - JOUR
AU  - E. A. Polyakov
AU  - M. G. Rozinas
TI  - Relationships between different forms of relative computability of functions
JO  - Sbornik. Mathematics
PY  - 1979
SP  - 425
EP  - 436
VL  - 35
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SM_1979_35_3_a6/
LA  - en
ID  - SM_1979_35_3_a6
ER  - 
%0 Journal Article
%A E. A. Polyakov
%A M. G. Rozinas
%T Relationships between different forms of relative computability of functions
%J Sbornik. Mathematics
%D 1979
%P 425-436
%V 35
%N 3
%U http://geodesic.mathdoc.fr/item/SM_1979_35_3_a6/
%G en
%F SM_1979_35_3_a6

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

This article studies connections between several enumeration reducibility relations (including reducibility relationships defined by recursive and $\mu$-recursive operators) on the set of all partial functions of one variable. Isomorphic embeddings between the semilattices of the corresponding degrees are established. In passing, a strengthening of the fundamental operator theorem is obtained. Figures: 3. Bibliography: 11 titles.

[1] G. I. Muzyukina, “O $\mu$-stepenyakh nerazreshimosti funktsii”, Uchenye zapiski Ivanovskogo gos. ped. in-ta, 125 (1973), 84–93

[2] E. A. Polyakov, M. G. Rozinas, Teoriya algoritmov, izd-vo Ivanovskogo un-ta, Ivanovo, 1976 | MR

[3] E. A. Polyakov, M. G. Rozinas, “Svodimosti po perechislimosti”, Sib. matem. zh., 18:4 (1977), 838–845 | MR | Zbl

[4] X. Rodzhers, Teoriya rekursivnykh funktsii i effektivnaya vychislimost, izd-vo “Mir”, Moskva, 1972 | MR

[5] M. G. Rozinas, “Chastichnye stepeni i $r$-stepeni”, Sib. matem. zh., 15:6 (1974), 1323–1331 | MR | Zbl

[6] D. G. Skordev, “Izchislimi i $\mu$-rekursivni operatori”, Izv. matem. in-t B'lgarsk. AN, 7 (1963), 5–43 | MR

[7] D. G. Skordev, “Nekotorye modeli kombinatornoi logiki”, Matem. zametki, 19:1 (1976), 149–154 | MR | Zbl

[8] I. Case, “Enumeration reductibility and partial degrees”, Ann. Math. Logic, 2:4 (1971), 419–439 | DOI | MR | Zbl

[9] L. P. Sasso, “A survey of partial degrees”, J. Symp. Logic, 40:2 (1975), 130–140 | DOI | MR | Zbl

[10] D. Skordev, “On Turing computable operations”, Godishnik na Sofiiskiya univ., 67 (1976), 103–112 | MR | Zbl

[11] V. Vuckovic, “Almost recursivity and partial degrees”, Z. Math. Logic Gr. Math., 20:5 (1974), 419–426 | DOI | MR | Zbl