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Computably Separable Models

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Abstract

We provide fundamental results of the structural theory of computably separable models and consider applications of this theory to the theory of effective linear orders and theoretical informatics.

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References

  1. W. Baur, “Rekursive Algebren mit Kettenbedingungen,” Z. Math. Logik Grundl. Math., 20, 37–46 (1974).

    Article  MathSciNet  Google Scholar 

  2. W. Baur, “Über rekursive Strukturen,” Invent. Math., 23, No. 2, 89–95 (1974).

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  4. M. Broy, W. Dosch, H. Partsch, P. Pepper, and M. Wirsing, “Existential quantifiers in abstract data types,” Lecture Notes in Comput. Sci., 71, 73–81 (1979).

    Article  MathSciNet  Google Scholar 

  5. Yu. L. Ershov, Numeration Theory [in Russian], Nauka, Moscow (1977).

  6. Yu. L. Ershov, Solvability Problems and Constructive Models [in Russian], Nauka, Moscow (1980).

  7. L. Feiner, “Hierarchies of Boolean algebras,” J. Symb. Logic, 35, No. 2, 365–373 (1970).

    Article  MathSciNet  Google Scholar 

  8. E. B. Fokina, B. Khoussainov, and P. D. Semukhin, “Linear orders realized by C. E. equivalence relations,” J. Symb. Logic, 81, No. 2, 463–482 (2016).

    Article  MathSciNet  Google Scholar 

  9. S. S. Goncharov, “Data models and languages for their description”, Vych. Sist. (Tr. IM SO AN SSSR), 107, 52–70(1985).

    MATH  Google Scholar 

  10. S. S. Goncharov and Yu. L. Ershov, Constructive Models [in Russian], Nauchnaya kniga, Novosibirsk (1999).

  11. S. Kamin, “Some definitions for algebraic data type specifications,” SIGPLAN Notes, 14, No. 3, 28–37 (1979).

    Article  Google Scholar 

  12. N. Kh. Kasymov, “On algebras with finitely approximable positively representable enrichments,” Algebra i Logika, 26, No. 6, 715–730 (1987).

    MathSciNet  MATH  Google Scholar 

  13. N. Kh. Kasymov, “Positive algebras with congruences of finite index,” Algebra i Logika, 30, No. 3, 293–305 (1991).

    MathSciNet  MATH  Google Scholar 

  14. N. Kh. Kasymov, “Positive algebras with countable congruence lattices,” Algebra i Logika, 31, No. 1, 21–37 (1992).

    MathSciNet  MATH  Google Scholar 

  15. N. Kh. Kasymov, “Positive algebras with Noetherian congruence lattices,” Sib. Mat. Zh., 33, No. 2, 181–185 (1992).

    Article  MathSciNet  Google Scholar 

  16. N. Kh. Kasymov, “On the number of congruences of algebras over simple sets,” Mat. Zametki, 52, No. 2, 150–152 (1992).

    MathSciNet  MATH  Google Scholar 

  17. N. Kh. Kasymov, “Homomorphisms onto negative algebras,” Algebra i Logika, 31, No. 2, 132–144 (1992).

    MathSciNet  MATH  Google Scholar 

  18. N. Kh. Kasymov, “Separation axioms and partitions of the set of natural numbers,” Sib. Mat. Zh., 34, No. 3, 81–85 (1993).

    Article  Google Scholar 

  19. N. Kh. Kasymov, “Enumerated algebras with uniformly recursive-separable classes,” Sib. Mat. Zh., 34, No. 5, 85–102 (1993).

    Article  Google Scholar 

  20. N. Kh. Kasymov, “Algebras over negative equivalences,” Algebra i Logika, 33, No. 1, 76–80 (1994).

    MathSciNet  MATH  Google Scholar 

  21. N. Kh. Kasymov, “Recursively separable enumerated algebras,” Usp. Mat. Nauk, 51, No. 3, 145–176 (1996).

    Article  MathSciNet  Google Scholar 

  22. N. Kh. Kasymov, “On computability of negative representations of the Goncharov standard model of arithmetics”, Proc. Int. Conf. Algebra, Analysis and Quantum Probability, Tashkent, 117–119 (2015).

  23. N. Kh. Kasymov, “Homomorphisms onto effectively separable algebras,” Sib. Mat. Zh., 57, No. 1, 47–66 ( 2016).

    Article  MathSciNet  Google Scholar 

  24. N. Kh. Kasymov and R. N. Dadazhanov, “Negative dense linear orders,” Sib. Mat. Zh., 58, No. 6, 1306–1331 (2017).

    Article  MathSciNet  Google Scholar 

  25. N. Kh. Kasymov and F. N. Ibragimov, “Structure characterization of the recursively separable models,” Dokl. AN RUS, No. 11, 14–16 (1998).

  26. N. Kh. Kasymov and A. S. Morozov, “Definability of linear orders over negative equivalences,” Algebra i Logika, 55, No. 1, 37–57 (2016).

    MathSciNet  MATH  Google Scholar 

  27. B. Khoussainov, T. Slaman, and P. Semukhin, “\( {\prod}_1^0-\mathrm{presentasions} \) of algebras,” Arch. Math. Logic, 45, No. 6, 769–781 (2006).

  28. A. I. Mal’tsev, “To general theory of algebraic systems,” Mat. Sb., 35, No. 1, 3–20 (1954).

    MathSciNet  MATH  Google Scholar 

  29. A. I. Mal’tsev, “Constructive algebras. I,” Usp. Mat. Nauk, 16, No. 3, 3–60 (1961).

    MathSciNet  MATH  Google Scholar 

  30. A. I. Mal’tsev, “Positive and negative numerations,” Dokl. AN SSSR, 160, No. 2, 278–280 (1965).

    MATH  Google Scholar 

  31. A. I. Mal’tsev, Algebraic Systems [in Russian], Nauka, Moscow (1970).

  32. A. I. Mal’tsev, Algorithms and Recursive Functions [in Russian], Nauka, Moscow (1986).

  33. P. Martin-Lef, Sketches on Constructive Mathematics [in Russian], Mir, Moscow (1975).

  34. A. S. Morozov and J. K. Truss, “On computable automorphisms of the rational numbers,” J. Symb. Logic, 66, No. 3, 1458–1470 (2001).

    Article  MathSciNet  Google Scholar 

  35. A. Nerode, “General topology and partial recursive functionals,” Talks Cornell Summ. Inst. Symb. Log., Cornell, 247–251 (1957).

  36. V. A. Uspenskiy, “On computable operations,” Dokl. AN SSSR, 103, No. 5, 773–776 (1955).

    MathSciNet  Google Scholar 

  37. V. A. Uspenskiy, “Systems of countable sets and their numerations,” Dokl. AN SSSR, 105, No. 6, 1155–1158 (1955).

    Google Scholar 

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Authors and Affiliations

  1. National University of Uzbekistan named after M. Ulugbek, Tashkent, Uzbekistan

    N. Kh. Kasymov & F. N. Ibragimov

Authors
  1. N. Kh. Kasymov
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  2. F. N. Ibragimov
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Correspondence to N. Kh. Kasymov.

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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 64, No. 4, Contemporary Problems of Mathematics and Physics, 2018.

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Kasymov, N.K., Ibragimov, F.N. Computably Separable Models. J Math Sci 264, 746–767 (2022). https://doi.org/10.1007/s10958-022-06033-1

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