Algebra and Logic

, Volume 46, Issue 3, pp 149–157 | Cite as

Spectra of computable models for Ehrenfeucht theories

  • A. N. Gavryushkin
Article

Abstract

We construct an example of a theory with a finite (greater than one) number of isomorphism types of countable models such that its prime and saturated models have computable presentations and there exists a model which lacks in such.

Keywords

Ehrenfeucht theory countable model computable presentation of a model 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    C. C. Chang and H. J. Keisler, Model Theory, 2nd edn., North Holland (1977).Google Scholar
  2. 2.
    S. S. Goncharov and Yu. L. Ershov, Constructive Models, Siberian School of Algebra and Logic [in Russian], Nauch. Kniga, Novosibirsk (1999).Google Scholar
  3. 3.
    H. Rogers, Theory of Recursive Functions and Effective Computability, McGraw-Hill, New York (1967).MATHGoogle Scholar
  4. 4.
    R. I. Soare, Recursively Enumerable Sets and Degrees, Springer, Berlin (1987).Google Scholar
  5. 5.
    M. G. Peretyatkin, “Complete theories with finite number of countable models,” Algebra Logika, 12, No. 5, 550–576 (1973).Google Scholar
  6. 6.
    M. Morley, “Decidable models,” Israel J. Math., 25, 233–240 (1976).MATHGoogle Scholar
  7. 7.
    B. Khoussainov, A. Nies, and R. A. Shore, “Computable models of theories with few models,” Notre Dame J. Formal Log., 38, No. 2, 165–178 (1997).MATHCrossRefGoogle Scholar
  8. 8.
    A. N. Gavryushkin, “Complexity of Ehrenfeucht models,” Algebra Logika, 45, No. 5, 507–519 (2006).Google Scholar
  9. 9.
    D. Marker, “Non-Σn-axiomatizable almost strongly minimal theories,” J. Symb. Log., 54, No. 3, 921–927 (1989).MATHCrossRefGoogle Scholar
  10. 10.
    S. S. Goncharov and B. Khoussainov, “Complexity of categorical theories with computable models,” Algebra Logika, 43, No. 6, 650–665 (2004).MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • A. N. Gavryushkin
    • 1
  1. 1.Novosibirsk State UniversityNovosibirskRussia

Personalised recommendations