Skip to main content
Log in

Turing Degrees of Complete Formulas of Almost Prime Models

  • COMMUNICATIONS
  • Published:
Algebra and Logic Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. S. S. Goncharov and Yu. L. Ershov, Constructive Models, Sib. School Alg. Log. [in Russian], Nauch. Kniga, Novosibirsk (1999).

    Google Scholar 

  2. A. I. Mal’tsev, “On recursive Abelian groups,” Dokl. Akad. Nauk SSSR, 146, No. 5, 1009-1012 (1962).

    MathSciNet  MATH  Google Scholar 

  3. A. I. Mal’tsev, “Constructive algebras. 1,” Usp. Mat. Nauk, 16, No. 3, 3-60 (1961).

    MathSciNet  Google Scholar 

  4. C. C. Chang and H. J. Keisler, Model Theory, North-Holland, Amsterdam (1973).

    MATH  Google Scholar 

  5. H. Rogers, Theory of Recursive Functions and Effective Computability, McGraw-Hill, New York (1967).

    MATH  Google Scholar 

  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.

  7. A. T. Nurtazin, “Strong and weak constructivizations and computable families,” Algebra and Logic, 13, No. 3, 177-184 (1974).

    Article  MathSciNet  Google Scholar 

  8. S. S. Goncharov, “The problem of the number of non-autoequivalent constructivizations,” Dokl. Akad. Nauk SSSR, 251, No. 2, 271-274 (1980).

    MathSciNet  Google Scholar 

  9. S. S. Goncharov, “Problem of number of nonautoequivalent constructivizations,” Algebra and Logic, 19, No. 6, 401-414 (1980).

    Article  MathSciNet  Google Scholar 

  10. S. S. Goncharov, “Groups with a finite number of constructivizations,” Dokl. Akad. Nauk SSSR, 256, No. 2, 269-272 (1981).

    MathSciNet  MATH  Google Scholar 

  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).

    Article  MathSciNet  Google Scholar 

  12. S. S. Goncharov, “Computable single-valued numerations,” Algebra and logic, 19, No. 5, 325-356 (1980).

    Article  Google Scholar 

  13. E. B. Fokina, I. Kalimullin, and R. Miller, “Degrees of categoricity of computable structures,” Arch. Math. Log., 49, No. 1, 51-67 (2010).

    Article  MathSciNet  Google Scholar 

  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).

    Article  MathSciNet  Google Scholar 

  15. N. A. Bazhenov, “Degrees of categoricity for superatomic Boolean algebras,” Algebra and Logic, 52, No. 3, 179-187 (2013).

    Article  MathSciNet  Google Scholar 

  16. B. Anderson and B. Csima, “Degrees that are not degrees of categoricity,” Notre Dame J. Form. Log., 57, No. 3, 389-398 (2016).

    MathSciNet  MATH  Google Scholar 

  17. E. Fokina, A. Frolov, and I. Kalimullin, “Categoricity spectra for rigid structures,” Notre Dame J. Form. Log., 57, No. 1, 45-57 (2016).

    Article  MathSciNet  Google Scholar 

  18. R. Miller, “d-Computable categoricity for algebraic fields,” J. Symb. Log.,74, No. 4, 1325-1351 (2009).

    Article  MathSciNet  Google Scholar 

  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.

  20. N. A. Bazhenov, “Autostability spectra for Boolean algebras,” Algebra and Logic, 53, No. 6, 502-505 (2014).

    Article  MathSciNet  Google Scholar 

  21. S. S. Goncharov, “Degrees of autostability relative to strong constructivizations,” Trudy MIAN, 274, 119-129 (2011).

    MathSciNet  MATH  Google Scholar 

  22. E. A. Palyutin, “Algebras of formulas for countably categorical theories,” Coll. Math., 31, 157-159 (1974).

    Article  Google Scholar 

  23. J. H. Schmerl, “A decidable ℵ0-categorical theory with a non-recursive Ryll-Nardzewski function,” Fund. Math., 98, No. 2, 121-125 (1978).

    Article  MathSciNet  Google Scholar 

  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.

  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).

  26. M. Morley, “Decidable models,” Israel J. Math., 25, Nos. 3/4, 233-240 (1976).

    Article  MathSciNet  Google Scholar 

  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.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S. S. Goncharov.

Additional information

*Supported by SB RAS Fundamental Research Program I.1.1 (project No. 0314-2019-0002), by RFBR (project No. 17-01-00247), and by NSF (grant DMS-1600625).

**Supported by Simons Foundation (grant No. 581896), by PSC-CUBY Research Bonuses, and by NSF (grant DMS-1600625).

***Supported by Simons Foundation (grant No. 429466), by NSF (grant DMS-1600625), by CCAS, and by Dean’s Research Chair.

Translated from Algebra i Logika, Vol. 58, No. 3, pp. 417-425,May-June, 2019.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Goncharov, S.S., Miller, R. & Harizanov, V. Turing Degrees of Complete Formulas of Almost Prime Models. Algebra Logic 58, 282–287 (2019). https://doi.org/10.1007/s10469-019-09546-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10469-019-09546-y

Navigation