Geodesic
On universal functions in hereditarily finite superstructures
Matematičeskie trudy, Tome 24 (2021) no. 2, pp. 160-180.

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

We obtain the necessary and sufficient condition for the existence of an universal $\Sigma$-function in the hereditarily finite superstructure. We show the application of this criterion to various well-known classes of structures. 
@article{MT_2021_24_2_a9,
     author = {A. N. Khisamiev},
     title = {On universal functions in hereditarily finite superstructures},
     journal = {Matemati\v{c}eskie trudy},
     pages = {160--180},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2021_24_2_a9/}
}
TY  - JOUR
AU  - A. N. Khisamiev
TI  - On universal functions in hereditarily finite superstructures
JO  - Matematičeskie trudy
PY  - 2021
SP  - 160
EP  - 180
VL  - 24
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MT_2021_24_2_a9/
LA  - ru
ID  - MT_2021_24_2_a9
ER  - 
%0 Journal Article
%A A. N. Khisamiev
%T On universal functions in hereditarily finite superstructures
%J Matematičeskie trudy
%D 2021
%P 160-180
%V 24
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MT_2021_24_2_a9/
%G ru
%F MT_2021_24_2_a9
A. N. Khisamiev. On universal functions in hereditarily finite superstructures. Matematičeskie trudy, Tome 24 (2021) no. 2, pp. 160-180. http://geodesic.mathdoc.fr/item/MT_2021_24_2_a9/

[1] Ershov Yu. L., Opredelimost i vychislimost, Nauchnaya kniga, Novosibirsk, 1996; Экономика, М., 2000

[2] Kalimullin I. Sh., Puzarenko V. G., “O vychislimosti na strukturakh”, Matem. tr., 7:2 (2004), 35–72

[3] Morozov A. S., Puzarenko V. G., “O $\Sigma$-podmnozhestvakh naturalnykh chisel”, Algebra i logika, 43:3 (2004), 291–320 | Zbl

[4] Puzarenko V. G., “K vychislimosti na spetsialnykh modelyakh”, Sib. matem. zhurn., 46:1 (2005), 185–208 | Zbl

[5] Rodzhers Kh., Teoriya rekursivnykh funktsii i effektivnaya vychislimost, Mir, M., 1972

[6] Rudnev V. A., “Ob universalnoi rekursivnoi funktsii na dopustimykh mnozhestvakh”, Algebra i logika, 25:4 (1986), 425–436

[7] Fuks L., Beskonechnye abelevy gruppy, v. 1, Mir, M., 1974

[8] Khisamiev A. N., “O verkhnei polureshetke Ershova”, Sib. matem. zhurn., 45:1 (2004), 211–228 | Zbl

[9] Khisamiev A. N., “O $\Sigma$-podmnozhestvakh naturalnykh chisel nad abelevymi gruppami”, Sib. matem. zhurn., 47:3 (2006), 695–706 | Zbl

[10] Khisamiev A. N., “$\Sigma$-ogranichennye algebraicheskie sistemy i universalnye funktsii. I”, Sib. matem. zhurn., 51:1 (2010), 217–235 | Zbl

[11] Khisamiev A. N., “$\Sigma$-ogranichennye algebraicheskie sistemy i universalnye funktsii. II”, Sib. matem. zhurn., 51:3 (2010), 676–693 | Zbl

[12] Khisamiev A. N., “Universalnye funktsii i $\Sigma_{\omega}$-ogranichennye struktury”, Algebra i logika, 60:2 (2021), 210–230 | Zbl

[13] Ershov Yu. L., Puzarenko V. G., Stukachev A. I., “HF-Computability”, Computability in Context: Computation and Logic in the Real World, eds. S. B. Cooper, A. Sorbi, Imperial College Press, London, 2011, 169–242 | DOI | Zbl