Geodesic
Computability and universal determinability of negatively representative models
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2022), pp. 22-32.

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

It has been established that a negative representable model is computable if and only if its standard enrichment with constants is isomorphically embedded in any model of a suitable computable enumerated set of universal sentences implemented in this model. It is shown that for computable enumerable sets of existential sentences this statement is incorrect.
Keywords: computable, negative and positive representations of models, standard enrichment, negative and positive diagram, universal and existential determinability. 
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R. N. Dadazhanov. Computability and universal determinability of negatively representative models. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2022), pp. 22-32. http://geodesic.mathdoc.fr/item/IVM_2022_10_a2/

[1] Goncharov S. S., Ershov Yu. L., Konstruktivnye modeli, Nauchn. kn., Novosibirsk, 1999

[2] Ershov Yu. L., Problemy razreshimosti i konstruktivnye modeli, Nauka, M., 1980

[3] Goncharov S. S., “Modeli dannykh i yazyki ikh opisanii”, Vychisl. sistemy, 107 (1985), 52–70 | Zbl

[4] Kasymov N. Kh., “Rekursivno otdelimye numerovannye algebry”, UMN, 51:3 (1996), 145–176 | MR | Zbl

[5] Maltsev A. I., “Konstruktivnye algebry. I”, UMN, 16:3 (1961), 3–60 | MR | Zbl

[6] Maltsev A. I., Algebraicheskie sistemy, Nauka, M., 1970 | MR

[7] Soar I. R., Vychislimo perechislimye mnozhestva i stepeni, Kazansk. matem. ob-vo, Kazan, 2000 | MR

[8] Kasymov N. Kh., Morozov A. S., “Logicheskie aspekty teorii abstraktnykh tipov dannykh”, Vychisl. sistemy, 122 (1987), 73–96 | Zbl

[9] Bergstra J. A., Tucker J. V., “A characterization of computable data types by means of a finite equational specification method”, Automata, Languages and Programming, ICALP 1980, Lect. Notes in Comput. Sci., 85, eds. de Bakker J., van Leeuwen J., Springer, Berlin–Heidelberg, 1980 | DOI | MR

[10] Kasymov N. Kh., “Ob algebrakh s finitno approksimiruemymi pozitivno predstavimymi obogascheniyami”, Algebra i logika, 26:6 (1987), 715–730 | MR

[11] Kasymov N. Kh., “Aksiomy otdelimosti i razbieniya naturalnogo ryada”, Sib. matem. zhurn., 34:3 (1993), 81–85 | MR | Zbl

[12] Kasymov N. Kh., “Numerovannye algebry s ravnomerno rekursivno otdelimymi klassami”, Sib. matem. zhurn., 34:5 (1993), 85–102 | MR | Zbl

[13] Kasymov N. Kh., “O gomomorfizmakh na effektivno otdelimye algebry”, Sib. matem. zhurn., 57:1 (2016), 47–66 | MR | Zbl

[14] Kasymov N. Kh., Ibragimov F. N., “Otdelimye numeratsii tel i effektivnaya vlozhimost v nikh kolets”, Sib. matem. zhurn., 60:1 (2019), 82–94 | MR | Zbl

[15] Kasymov N. Kh., “O gomomorfizmakh na negativnye algebry”, Algebra i logika, 31:2 (1992), 132–144 | MR | Zbl

[16] Kasymov N. Kh., Ibragimov F. N., “Vychislimo otdelimye modeli”, SMFN, 64, no. 4, 2018, 682–705

[17] Kasymov N. Kh., Khodzhamuratova I. A., “Topologicheskie prostranstva nad algoritmicheskimi predstavleniyami universalnykh algebr”, Itogi nauki i tekhniki. Ser. Sovrem. matem. i ee prilozh. Temat. obz., 144, 2018, 17–29

[18] Kasymov N. Kh., “Ob algebrakh nad negativnymi ekvivalentnostyami”, Algebra i logika, 33:1 (1994), 76–80 | MR | Zbl

[19] Kasymov N. Kh., “Pozitivnye algebry s kongruentsiyami konechnogo indeksa”, Algebra i logika, 30:3 (1991), 293–305 | MR

[20] Kasymov N. Kh., “Pozitivnye algebry so schetnymi reshetkami kongruentsii”, Algebra i logika, 31:1 (1992), 21–37 | MR | Zbl

[21] Ershov Yu. L., Teoriya numeratsii, Nauka, M., 1977 | MR

[22] Kasymov N. Kh., Dadazhanov R. N., Dzhavliev S. K., “Struktury stepenei negativnoi predstavimosti lineinykh poryadkov”, Izv. vuzov. Matem., 2021, no. 12, 31–55 | Zbl

[23] Khoussainov B. M., Slaman T., Semukhin P., “$\prod_1^0$-Presentasions of Algebras”, Archive Math. Logic, 45:6 (2006), 769–781 | DOI | MR | Zbl

[24] Kasymov N. Kh., Dadazhanov R. N., “Negativnye plotnye lineinye poryadki”, Sib. matem. zhurn., 58:6 (2017), 1306–1331 | MR | Zbl

[25] Kasymov N. Kh., Morozov A. S., “Ob opredelimosti lineinykh poryadkov nad negativnymi ekvivalentnostyami”, Algebra i logika, 55:1 (2016), 37–57 | MR | Zbl