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Some Properties of the Upper Semilattice of Computable Families of Computably Enumerable Sets

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Algebra and Logic Aims and scope

We look at specific features of the algebraic structure of an upper semilattice of computable families of computably enumerable sets in Ω. It is proved that ideals of minuend and finite families of Ω coincide. We deal with the question whether there exist atoms and coatoms in the factor semilattice of Ω with respect to an ideal of finite families. Also we point out a sufficient condition for computable families to be complemented.

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References

  1. Yu. L. Ershov, Theory of Numerations [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  2. A. N. Degtev, “The semilattice of computable families of recursively enumerable sets,” Mat. Zametki, 50, No. 4, 61-66 (1991).

    MathSciNet  MATH  Google Scholar 

  3. R. I. Soare, Recursively Enumerable Sets and Degrees, Perspect. Math. Log., Omega Ser., Springer-Verlag, Heidelberg (1987).

  4. S. A. Badaev, “Positive enumerations,” Sib. Math. J., 18, No. 3, 343-352 (1977).

    Article  Google Scholar 

  5. S. A. Badaev and S. S. Goncharov, “Generalized computable universal numberings,” Algebra and Logic, 53, No. 5, 355-364 (2014).

    Article  MathSciNet  Google Scholar 

  6. R. F. Friedberg, “Three theorems on recursive enumeration. I. Decomposition. II. Maximal set. III. Enumeration without duplication,” J. Symb. Log., 23, No. 3, 309-316 (1958).

    Article  MathSciNet  Google Scholar 

  7. C. E. Yates, “On the degrees of index sets. II,” Trans. Am. Math. Soc., 135, 249-266 (1969).

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Kazan (Volga Region) Federal University, Kazan, Russia

    M. Kh. Faizrakhmanov

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  1. M. Kh. Faizrakhmanov
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Correspondence to M. Kh. Faizrakhmanov.

Additional information

Translated from Algebra i Logika, Vol. 60, No. 2, pp. 195-209, March-April, 2021. Russian https://doi.org/10.33048/alglog.2021.60.206.

The work was carried out as part of the developmental program for the Science Education Mathematical Center (SEMC) in Volga Federal District, Agreement No. 075-02-2021-1393, and supported by Russian Science Foundation, project No. 18-01-00028.

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Faizrakhmanov, M.K. Some Properties of the Upper Semilattice of Computable Families of Computably Enumerable Sets. Algebra Logic 60, 128–138 (2021). https://doi.org/10.1007/s10469-021-09635-x

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  • DOI: https://doi.org/10.1007/s10469-021-09635-x

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