Algebra and Logic

, 50:279 | Cite as

Turing jumps in the Ershov hierarchy

  • M. Kh. FaizrakhmanovEmail author

We look at infinite levels of the Ershov hierarchy in the natural system of notation, which are proper for jumps of sets. It is proved that proper infinite levels for jumps are confined to \( \Delta_a^{ - 1} \) -levels, where a stands for an ordinal ωn > 1.


Turing jumps Ershov hierarchy constructive ordinals superlow sets 


  1. 1.
    Yu. L. Ershov, “On a hierarchy of sets I,” Algebra Logika, 7, No. 1, 47–73 (1968).zbMATHGoogle Scholar
  2. 2.
    Yu. L. Ershov, “On a hierarchy of sets II,” Algebra Logika, 7, No. 4, 15–47 (1968).zbMATHGoogle Scholar
  3. 3.
    Yu. L. Ershov, “On a hierarchy of sets III,” Algebra Logika, 9, No. 1, 34–51 (1970).MathSciNetGoogle Scholar
  4. 4.
    M. M. Arslanov, The Ershov Hierarchy, A Special Course in Mathematics, Kazan State Univ., Kazan (2007).Google Scholar
  5. 5.
    H. G. Carstens, “\( \Delta_2^0 \) -Mengen,” Arch. Math. Logik Grundl., 18, 55–65 (1976).MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    B. Schaeffer, “Dynamic notions of genericity and array noncomputability,” Ann. Pure Appl. Log., 95, Nos. 1–3, 37–69 (1998).MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    S. Walk, “Towards a definition of the array computable degrees,” Ph. D. Thesis, Univ. Notre Dame (1999).Google Scholar
  8. 8.
    I. Sh. Kalimullin, “Some notes on degree spectra of the structures,” Lect. Notes Comput. Sci., 4497, Springer-Verlag, Berlin (2007), pp. 389–397.Google Scholar

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© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.Kazan (Volga Region) Federal UniversityKazanRussia

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