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Semidecidable Numberings in Admissible Sets

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References

  1. 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).

    MathSciNet  MATH  Google Scholar 

  2. Yu. L. Ershov, Definability and Computability, Siberian School of Algebra and Logic [in Russian], Nauch. Kniga, Novosibirsk (1996).

  3. V. G. Puzarenko, “Decidable computable \( \mathbbm{A} \)-numberings,” Algebra and Logic, 41, No. 5, 314-322 (2002).

    MathSciNet  MATH  Google Scholar 

  4. V. G. Puzarenko, “Computability in special models,” Sib. Math. J., 46, No. 1, 148-165 (2005).

    MathSciNet  MATH  Google Scholar 

  5. I. Sh. Kalimullin, V. G. Puzarenko, and M. Kh. Faizrakhmanov, “Positive presentations of families relative to e-oracles,” Sib. Math. J., 59, No. 4, 648-656 (2018).

    MathSciNet  MATH  Google Scholar 

  6. I. Sh. Kalimullin, V. G. Puzarenko, and M. Kh. Faizrakhmanov, “Computable positive and Friedberg numberings in hyperarithmetic,” Algebra and Logic, 59, No. 1, 46-58 (2020).

    Google Scholar 

  7. I. Sh. Kalimullin, V. G. Puzarenko, and M. Kh. Faizrakhmanov, “Positive numberings in admissible sets,” Sib. Math. J., 61, No. 3, 478-489 (2020).

    MATH  Google Scholar 

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

  9. D. Marker, “Non-Σn-axiomatizable almost strongly minimal theories,” J. Symb. Log., 54, No. 3, 921-927 (1989).

    MathSciNet  MATH  Google Scholar 

  10. S. S. Goncharov and B. Khoussainov, “Complexity of theories of computable categorical models,” Algebra and Logic, 43, No. 6, 365-373 (2004).

    MathSciNet  Google Scholar 

  11. M. Faizrahmanov, A. Kach, I. Kalimullin, A. Montalbán, and V. Puzarenko, “Jump inversions of algebraic structures and Σ-definability,” Math. Log. Q., 65, No. 1, 37-45 (2019).

    MathSciNet  MATH  Google Scholar 

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Correspondence to I. Sh. Kalimullin.

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I. Sh. Kalimullin is supported by Russian Science Foundation, (project No. 18-11-00028) and by the Russian Ministry of Education and Science (project No. 1.451.2016/1.4).

V. G. Puzarenko is supported by RFBR (project No. 18-01-00624) and by SB RAS Fundamental Research Program I.1.1 (project No. 0314-2019-0003).

M. Kh. Faizrakhmanov is supported by a Funding Program for the Regional Scientific and Educational Mathematical Center of the Volga Federal Region, Agreement No. 075-02-2020-1478.

Translated from Algebra i Logika, Vol. 59, No. 3, pp. 395-402, May-June, 2020. Russian https://doi.org/10.33048/alglog.2020.59.308.

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Kalimullin, I.S., Puzarenko, V.G. & Faizrakhmanov, M.K. Semidecidable Numberings in Admissible Sets. Algebra Logic 59, 273–277 (2020). https://doi.org/10.1007/s10469-020-09599-4

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  • DOI: https://doi.org/10.1007/s10469-020-09599-4

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