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Uniformly Computably Separable Algebras with Effectively Splittable Families of Negative Congruences

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Abstract

We characterize uniformly computably separable algebras with effectively splittable families of negative congruences and study certain properties similar to productivity.

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References

  1. Soare R. I., Recursively Enumerable Sets and Degrees: A Study of Computable Functions and Computably Generated Sets, Springer, Heidelberg (1987).

    Book  Google Scholar 

  2. Rogers H., Theory of Recursive Functions and Effective Computability, McGraw-Hill, New York, St. Louis, San Francisco, Toronto, London, and Sydney (1967).

    MATH  Google Scholar 

  3. Ershov Yu. L., The Theory of Enumerations, Nauka, Moscow (1977) [Russian].

    Google Scholar 

  4. Ershov Yu. L., Decision Problems and Constructive Models, Nauka, Moscow (1980) [Russian].

    Google Scholar 

  5. Ershov Yu. L. and Goncharov S. S., Constructive Models, Kluwer Academic/Plenum, New York, etc. (2000) (Siberian School of Algebra Logic).

    Book  Google Scholar 

  6. Maltsev A. I., “Constructive algebras. I,” Russian Math. Surveys, vol. 16, no. 3, 77–129 (1961).

    Article  MathSciNet  Google Scholar 

  7. Andrews U. and Sorbi A., “Jumps of computably enumerable equivalence relations,” Ann. Pure Appl. Logic, vol. 169, no. 3, 243–259 (2017).

    Article  MathSciNet  Google Scholar 

  8. Andrews U. and Sorbi A., “Joins and meets in the structure of ceers,” Computability, vol. 8, no. 3, 193–241 (2019).

    Article  MathSciNet  Google Scholar 

  9. Andrews U. and Badaev S., “On isomorphism classes of computably enumerable equivalence relations,” J. Symb. Logic, vol. 85, no. 1, 1–26 (2019).

    MathSciNet  MATH  Google Scholar 

  10. Lempp S., Andrews U., Mustafa M., and Schweber N., “The first-order theory of the computably enumerable equivalence relations in the uncountable setting,” J. Logic Comput., vol. 32, no. 1, 98–114 (2022).

    Article  MathSciNet  Google Scholar 

  11. Gavryushkin A., Jain S., Khoussainov B., and Stephan F., “Graphs realised by r.e. equivalence relations,” Ann. Pure Appl. Logic, vol. 165, no. 7–8, 1263–1290 (2014).

    Article  MathSciNet  Google Scholar 

  12. Gavryushkin A., Khoussainov B., and Stephan F., “Reducibilities among equivalence relations induced by recursively enumerable structures,” Theoret. Comput. Sci., vol. 612, 137–152 (2016).

    Article  MathSciNet  Google Scholar 

  13. Kasymov N., Dadazhanov R., and Zhavliev S., “Structures of degrees of negative representations of linear orders,” Russian Math., vol. 65, no. 12, 27–46 (2021).

    Article  Google Scholar 

  14. Kasymov N. Kh., “Recursively separable enumerated algebras,” Russian Math. Surveys, vol. 51, no. 3, 509–538 (1996).

    Article  MathSciNet  Google Scholar 

  15. Kasymov N. Kh., Dadazhanov R. N., and Ibragimov F. N., “Separable algorithmic representations of classical systems and their applications,” Contemporary Mathematics. Fundamental Trends, vol. 67, no. 4, 707–754 (2021).

    Article  MathSciNet  Google Scholar 

  16. Kasymov N. Kh., “Positive algebras with congruences of finite index,” Algebra Logic, vol. 30, no. 3, 190–199 (1991).

    Article  MathSciNet  Google Scholar 

  17. Kasymov N. Kh., “Positive algebras with countable congruence lattices,” Algebra Logic, vol. 31, no. 1, 12–23 (1992).

    Article  MathSciNet  Google Scholar 

  18. Kasymov N. Kh., “Positive algebras with Noetherian congruence lattices,” Sib. Math. J., vol. 33, no. 2, 338–341 (1992).

    Article  MathSciNet  Google Scholar 

  19. Kasymov N. Kh., “The number of algebras over simple sets,” Math. Notes, vol. 52, no. 2, 861–862 (1992).

    Article  MathSciNet  Google Scholar 

  20. Kasymov N. Kh., “The number of \( Q \)-congruences in positive algebras,” Algebra Logic, vol. 31, no. 3, 182–187 (1992).

    Article  MathSciNet  Google Scholar 

  21. Bergstra J. A. and Tucker J. V., “A characterization of computable data types by means of a finite, equational specification method,” Lect. Notes Comput. Sci., vol. 85, 76–90 (1980).

    Article  Google Scholar 

  22. Kasymov N. Kh., “Algebras with finitely approximable positively representable enrichments,” Algebra Logic, vol. 26, no. 6, 441–450 (1987).

    Article  Google Scholar 

  23. Khoussainov B. and Miasnikov A., “Finitely presented expansions of groups, semigroups, and algebras,” Trans. Amer. Math. Soc., vol. 366, no. 3, 1455–1474 (2014).

    Article  MathSciNet  Google Scholar 

  24. Kasymov N. Kh., “Homomorphisms onto negative algebras,” Algebra Logic, vol. 31, no. 2, 81–89 (1992).

    Article  MathSciNet  Google Scholar 

  25. Kasymov N. Kh., “Enumerated algebras with uniformly recursive-separable classes,” Sib. Math. J., vol. 34, no. 5, 869–882 (1993).

    Article  MathSciNet  Google Scholar 

  26. Khoussainov B., “A journey to computably enumerable structures (Tutorial lectures),” Lect. Notes Comput. Sci., vol. 10936, 1–19 (2018).

    Article  MathSciNet  Google Scholar 

  27. Kasymov N. Kh. and Morozov A. S., “Definability of linear orders over negative equivalences,” Algebra Logic, vol. 55, no. 1, 24–37 (2016).

    Article  MathSciNet  Google Scholar 

  28. Kasymov N. Kh., “Algebras over negative equivalences,” Algebra Logic, vol. 33, no. 1, 46–48 (1994).

    Article  MathSciNet  Google Scholar 

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Correspondence to R. N. Dadazhanov.

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Translated from Sibirskii Matematicheskii Zhurnal, 2022, Vol. 63, No. 3, pp. 562–575. https://doi.org/10.33048/smzh.2022.63.307

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Dadazhanov, R.N., Kasymov, N.K. & Khodzhamuratova, I.A. Uniformly Computably Separable Algebras with Effectively Splittable Families of Negative Congruences. Sib Math J 63, 466–475 (2022). https://doi.org/10.1134/S0037446622030077

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  • DOI: https://doi.org/10.1134/S0037446622030077

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