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The Index Set of the Class of Autostable Ordered Abelian Groups

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Abstract

We find an exact estimate for the algorithmic complexity of the class of autostable ordered Abelian groups.

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REFERENCES

  1. R. G. Downey, S. S. Goncharov, A. M. Kach, J. F. Knight, O. V. Kudinov, A. G. Melnikov, and D. Turetsky, “Decidability and computability of certain torsion-free abelian groups,” Notre Dame J. Formal Logic 51, 85 (2010).

    MathSciNet  MATH  Google Scholar 

  2. R. G. Downey, A. M. Kach, S. Lempp, A. E. M. Lewis-Pye, A Montalbá’n, and D. D. Turetsky, “The complexity of computable categoricity,” Adv. Math. 268, 423 (2015).

    Article  MathSciNet  Google Scholar 

  3. Yu. L. Ershov and S. S. Goncharov, Constructive Models (Nauchnaya Kniga, Novosibirsk, 1999) [Constructive Models (Consultants Bureau, New York, 2000)].

  4. S. S. Goncharov, “Problem of the number of non-self-equivalent constructivizations,” Algebra i logika 19, 621 (1980) [Algebra and Logic 19, 401 (1980)].

    Article  Google Scholar 

  5. S. S. Goncharov, “ The problem of the number of nonautoequivalent constructivizations,” Dokl. Akad. Nauk SSSR 251, 271 (1980) [Soviet Math., Dokl. 21, 411 (1980)].

    MATH  Google Scholar 

  6. S. S. Goncharov, “Autostability of prime models under strong constructivizations,” Algebra i logika 48, 729 (2009) [Algebra and Logic 48, 410 (2009)].

    Article  MathSciNet  Google Scholar 

  7. S. S. Goncharov, “On autostability of almost prime models relative to strong constructivizations,” Uspekhi Mat. Nauk 65, no. 5, 107 (2010) [Russian Math. Surveys 65, 901 (2010)].

    Article  MathSciNet  Google Scholar 

  8. S. S. Goncharov, N. A. Bazhenov, and M. I. Marchuk, “The index set of Boolean algebras autostable relative to strong constructivizations,” Sib. Matem. Zh. 56, 498 (2015) [Siberian Math. J. 56, 393 (2015)].

    Article  MathSciNet  Google Scholar 

  9. S. S. Goncharov, N. A. Bazhenov, and M. I. Marchuk, “The index set of linear orderings that are autostable relative to strong constructivizations,” Vestnik Novosibirsk. Gos. Univ., Ser. Mat. Mekh. Inform. 15:3, 51 (2015) [in Russian].

    MATH  Google Scholar 

  10. S. S. Goncharov, N. A. Bazhenov, and M. I. Marchuk, “The index set of the groups autostable relative to strong constructivizations,” Sib. Matem. Zh. 58, 95 (2017) [Siberian Math. J. 58, 72 (2017)].

    Article  MathSciNet  Google Scholar 

  11. S. S. Goncharov and J. F. Knight, “Computable structure and non-structure theorems,” Algebra i logika 41, 639 (2002) [Algebra and Logic 41, 351 (2002)].

    Article  MathSciNet  Google Scholar 

  12. S. S. Goncharov, S. Lempp, and R. A. Solomon, “The computable dimension of ordered abelian groups,” Adv. Math. 175, 102 (2003).

    Article  MathSciNet  Google Scholar 

  13. S. S. Goncharov and M. I. Marchuk, “Index sets of constructive models of bounded signature that are autostable relative to strong constructivizations,” Algebra i logika 54, 163 (2015) [Algebra and Logic 54, 108 (2015)].

    Article  MathSciNet  Google Scholar 

  14. S. S. Goncharov and M. I. Marchuk, “Index sets of constructive models of finite and graph signatures that are autostable relative to strong constructivizations,” Algebra i logika 54, 663 (2015) [Algebra and Logic 54, 428 (2015)].

    Article  MathSciNet  Google Scholar 

  15. M. I. Marchuk, “Index set of structures with two equivalence relations that are autostable relative to strong constructivizations,” Algebra i logika 55, 465 (2016) [Algebra and Logic 55, 306 (2016)].

    Article  MathSciNet  Google Scholar 

  16. A. G. Melnikov, “Computable ordered abelian groups and fields,” in: Programs, Proofs, Processes (Proc. \(6\)th Conf. Comput. Europe), 321 (Springer, Berlin, 2010).

  17. A. G. Melnikov and K. M. Ng, “Computable torsion abelian groups,” Adv. Math. 325, 864 (2018).

    Article  MathSciNet  Google Scholar 

  18. A. T. Nurtazin, Computable Classes and Algebraic Criteria of Autostability (Ph. D. Thesis, Inst. Mat. Mekh., Alma-Ata, 1974) [in Russian].

  19. R. I. Soare, Turing Computability. Theory and Applications (Springer, Berlin, 2016).

    MATH  Google Scholar 

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ACKNOWLEDGMENTS

The author is grateful to Sergeĭ S. Goncharov and Nikolaĭ A. Bazhenov for useful discussions

Funding

The work was partially supported by the Russian Foundation for Basic Research (project 17-01-00247).

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia

    M. I. Marchuk

  2. Novosibirsk State University, Novosibirsk, 630090, Russia

    M. I. Marchuk

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  1. M. I. Marchuk
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Correspondence to M. I. Marchuk.

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Marchuk, M.I. The Index Set of the Class of Autostable Ordered Abelian Groups. Sib. Adv. Math. 31, 40–44 (2021). https://doi.org/10.1134/S1055134421010041

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  • DOI: https://doi.org/10.1134/S1055134421010041

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