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Algebra and Logic

, Volume 57, Issue 5, pp 392–396 | Cite as

Computable Bi-Embeddable Categoricity

  • N. A. Bazhenov
  • E. B. Fokina
  • D. Rossegger
  • L. San Mauro
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References

  1. 1.
    A. Montalbàn, “Up to equimorphism, hyperarithmetic is recursive,” J. Symb. Log., 70, No. 2, 360-378 (2005).MathSciNetCrossRefGoogle Scholar
  2. 2.
    A. Montalbàn, “On the equimorphism types of linear orderings,” Bull. Symb. Log., 13, No. 1, 71-99 (2007).MathSciNetCrossRefGoogle Scholar
  3. 3.
    N. Greenberg and A. Montalbán, “Ranked structures and arithmetic transfinite recursion,” Trans. Am. Math. Soc., 360, No. 3, 1265-1307 (2008).MathSciNetCrossRefGoogle Scholar
  4. 4.
    E. Fokina, D. Rossegger, and L. San Mauro, “Bi-embeddability spectra and bases of spectra,” arXiv:1808.05451 [math.LO].Google Scholar
  5. 5.
    E. B. Fokina, I. Kalimullin, and R. Miller, “Degrees of categoricity of computable structures,” Arch. Math. Log., 49, No. 1, 51-67 (2010).MathSciNetCrossRefGoogle Scholar
  6. 6.
    B. F. Csima, J. N. Franklin, and R. A. Shore, “Degrees of categoricity and the hyperarithmetic hierarchy,” Notre Dame J. Formal Log., 54, No. 2, 215-231 (2013).MathSciNetCrossRefGoogle Scholar
  7. 7.
    C. J. Ash and J. F. Knight, Computable Structures and the Hyperarithmetical Hierarchy, Stud. Log. Found. Math., Vol. 144, Elsevier, Amsterdam (2000).Google Scholar
  8. 8.
    N. A. Bazhenov, “Effective categoricity for distributive lattices and Heyting algebras,” Lobachevskii J. Math., 38, No. 4, 600-614 (2017).MathSciNetCrossRefGoogle Scholar
  9. 9.
    N. Bazhenov, E. Fokina, D. Rossegger, and L. San Mauro, “Degrees of biembeddability categoricity of equivalence structures,” Arch. Math. Log. (2018);  https://doi.org/10.1007/s00153-018-0650-3.
  10. 10.
    S. S. Goncharov and V. D. Dzgoev, “Autostability of models,” Algebra and Logic, 19, No. 1, 28-36 (1980).MathSciNetCrossRefGoogle Scholar
  11. 11.
    J. B. Remmel, “Recursive isomorphism types of recursive Boolean algebras,” J. Symb. Log., 46, No. 3, 572-594 (1981).MathSciNetCrossRefGoogle Scholar
  12. 12.
    J. B. Remmel, “Recursively categorical linear orderings,” Proc. Am. Math. Soc., 83, No. 2, 387-391 (1981).MathSciNetCrossRefGoogle Scholar
  13. 13.
    R. G. Downey, A.M. Kach, S. Lempp, A. E. M. Lewis-Pye, A. Montalbán, and D. D. Turetsky, “The complexity of computable categoricity,” Adv. Math., 268, 423-466 (2015).MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • N. A. Bazhenov
    • 1
    • 2
  • E. B. Fokina
    • 3
  • D. Rossegger
    • 3
  • L. San Mauro
    • 3
  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia
  3. 3.Institute of Discrete Mathematics and GeometryVienna University of TechnologyViennaAustria

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