Algebra and Logic

, Volume 58, Issue 3, pp 282–287 | Cite as

Turing Degrees of Complete Formulas of Almost Prime Models

  • S. S. GoncharovEmail author
  • R. Miller
  • V. Harizanov


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. S. Goncharov and Yu. L. Ershov, Constructive Models, Sib. School Alg. Log. [in Russian], Nauch. Kniga, Novosibirsk (1999).Google Scholar
  2. 2.
    A. I. Mal’tsev, “On recursive Abelian groups,” Dokl. Akad. Nauk SSSR, 146, No. 5, 1009-1012 (1962).MathSciNetzbMATHGoogle Scholar
  3. 3.
    A. I. Mal’tsev, “Constructive algebras. 1,” Usp. Mat. Nauk, 16, No. 3, 3-60 (1961).MathSciNetGoogle Scholar
  4. 4.
    C. C. Chang and H. J. Keisler, Model Theory, North-Holland, Amsterdam (1973).zbMATHGoogle Scholar
  5. 5.
    H. Rogers, Theory of Recursive Functions and Effective Computability, McGraw-Hill, New York (1967).zbMATHGoogle Scholar
  6. 6.
    S. Goncharov and B. Khoussainov, “Open problems in the theory of constructive algebraic systems,” Cont. Math., 257, Am. Math. Soc., Providence, RI (2000), pp. 145-170.Google Scholar
  7. 7.
    A. T. Nurtazin, “Strong and weak constructivizations and computable families,” Algebra and Logic, 13, No. 3, 177-184 (1974).MathSciNetCrossRefGoogle Scholar
  8. 8.
    S. S. Goncharov, “The problem of the number of non-autoequivalent constructivizations,” Dokl. Akad. Nauk SSSR, 251, No. 2, 271-274 (1980).MathSciNetGoogle Scholar
  9. 9.
    S. S. Goncharov, “Problem of number of nonautoequivalent constructivizations,” Algebra and Logic, 19, No. 6, 401-414 (1980).MathSciNetCrossRefGoogle Scholar
  10. 10.
    S. S. Goncharov, “Groups with a finite number of constructivizations,” Dokl. Akad. Nauk SSSR, 256, No. 2, 269-272 (1981).MathSciNetzbMATHGoogle Scholar
  11. 11.
    S. S. Goncharov, A. V. Molokov, and N. S. Romanovskii, “Nilpotent groups of finite algorithmic dimension,” Sib. Math. J., 30, No. 1, 63-68 (1989).MathSciNetCrossRefGoogle Scholar
  12. 12.
    S. S. Goncharov, “Computable single-valued numerations,” Algebra and logic, 19, No. 5, 325-356 (1980).CrossRefGoogle Scholar
  13. 13.
    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
  14. 14.
    B. F. Csima, J. N. Franklin, and R. A. Shore, “Degrees of categoricity and the hyperarithmetic hierarchy,” Notre Dame J. Form. Log., 54, No. 2, 215-231 (2013).MathSciNetCrossRefGoogle Scholar
  15. 15.
    N. A. Bazhenov, “Degrees of categoricity for superatomic Boolean algebras,” Algebra and Logic, 52, No. 3, 179-187 (2013).MathSciNetCrossRefGoogle Scholar
  16. 16.
    B. Anderson and B. Csima, “Degrees that are not degrees of categoricity,” Notre Dame J. Form. Log., 57, No. 3, 389-398 (2016).MathSciNetzbMATHGoogle Scholar
  17. 17.
    E. Fokina, A. Frolov, and I. Kalimullin, “Categoricity spectra for rigid structures,” Notre Dame J. Form. Log., 57, No. 1, 45-57 (2016).MathSciNetCrossRefGoogle Scholar
  18. 18.
    R. Miller, “d-Computable categoricity for algebraic fields,” J. Symb. Log.,74, No. 4, 1325-1351 (2009).MathSciNetCrossRefGoogle Scholar
  19. 19.
    E. B. Fokina, V. Harizanov, and A. Melnikov, “Computable model theory,” in Turing’s Legacy: Developments from Turing’s Ideas in Logic, Lect. Notes Log., 42, R. Downey (ed.), Cambridge Univ. Press, Ass. Symb. Log., Cambridge (2014), pp. 124-194.Google Scholar
  20. 20.
    N. A. Bazhenov, “Autostability spectra for Boolean algebras,” Algebra and Logic, 53, No. 6, 502-505 (2014).MathSciNetCrossRefGoogle Scholar
  21. 21.
    S. S. Goncharov, “Degrees of autostability relative to strong constructivizations,” Trudy MIAN, 274, 119-129 (2011).MathSciNetzbMATHGoogle Scholar
  22. 22.
    E. A. Palyutin, “Algebras of formulas for countably categorical theories,” Coll. Math., 31, 157-159 (1974).CrossRefGoogle Scholar
  23. 23.
    J. H. Schmerl, “A decidable ℵ0-categorical theory with a non-recursive Ryll-Nardzewski function,” Fund. Math., 98, No. 2, 121-125 (1978).MathSciNetCrossRefGoogle Scholar
  24. 24.
    N. Bazhenov, “Prime model with no degree of autostability relative to strong constructivizations,” in Lect. Notes Comput. Sci., 9136, Springer-Verlag, Berlin (2015), pp. 117-126.Google Scholar
  25. 25.
    S. S. Goncharov, “On the autostability of almost prime models relative to strong constructivizations,” Usp. Mat. Nauk, 65, No. 5(395), 107-142 (2010).Google Scholar
  26. 26.
    M. Morley, “Decidable models,” Israel J. Math., 25, Nos. 3/4, 233-240 (1976).MathSciNetCrossRefGoogle Scholar
  27. 27.
    R. Miller, “Revisiting uniform computable categoricity: For the sixtieth birthday of prof. Rod Downey,” Lect. Notes Comp. Sci., 10010, Springer, Cham (2017), pp. 254-270.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia
  3. 3.Queens College–C.U.N.YNew YorkUSA
  4. 4.C.U.N.Y. Graduate CenterNew YorkUSA
  5. 5.George Washington UniversityWashingtonUSA

Personalised recommendations