Algebra and Logic

, Volume 45, Issue 5, pp 289–295 | Cite as

Complexity of Ehrenfeucht models

  • A. N. Gavryushkin


We look at examples of Ehrenfeucht theories possessing constructive models and countable models of different complexities, and estimate complexity of the Ehrenfeucht theories having constructive models.


Ehrenfeucht theory constructive model 


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  1. 1.
    B. Hart, E. Hrushovski, and M. S. Laskowski, “The uncountable spectra of countable theories,” Ann. Math. (2), 152, No. 1, 207–257 (2000).MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    M. Lerman and J. Scmerl, “Theories with recursive models,” J. Symb. Log., 44, No. 1, 59–76 (1979).CrossRefMATHGoogle Scholar
  3. 3.
    J. Knight, “Nonarithmetical ℵ0-categorical theories with recursive models,” J. Symb. Log., 59, No. 1, 106–112 (1994).MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    S. S. Goncharov and B. Khoussainov, “On complexity of theories of computable ℵ1-categorical models,” Vestnik NGU, Mat., Mekh., Inf., 1, No. 2, 63–76 (2001).MATHGoogle Scholar
  5. 5.
    S. S. Goncharov and B. Khoussainov, “Complexity of categorical theories with computable models,” Algebra Logika, 43, No. 6, 650–665 (2004).MathSciNetMATHGoogle Scholar
  6. 6.
    C. C. Chang and H. J. Keisler, Model Theory, 3d edn., Stud. Log. Found. Math., Vol. 73, North-Holland, Amsterdam (1990).MATHGoogle Scholar
  7. 7.
    S. S. Goncharov and Yu. L. Ershov, Constructive Models, Siberian School of Algebra and Logic [in Russian], Nauch. Kniga, Novosibirsk (1999).Google Scholar
  8. 8.
    H. Rogers, Theory of Recursive Functions and Effective Computability, McGraw-Hill, New York (1967).MATHGoogle Scholar
  9. 9.
    R. I. Soare, Recursively Enumerable Sets and Degrees, A Study of Computable Functions and Computably Generated Sets, Springer, Berlin (1987).Google Scholar
  10. 10.
    R. Vaught, “Denumerable models of complete theories,” in Infinitistic Methods, Pergamon, London (1961), pp. 303–321.Google Scholar
  11. 11.
    M. G. Peretyatkin, “Complete theories with a finite number of countable models,” Algebra Logika, 12, No. 5, 550–576 (1973).Google Scholar
  12. 12.
    R. Reed, “A decidable Ehrenfeucht theory with exactly two hyperarithmetic models,” Ann. Pure Appl. Log., 53, No. 2, 135–168 (1991).CrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • A. N. Gavryushkin
    • 1
  1. 1.Institute of Mathematics, Siberian BranchRussian Academy of SciencesNovosibirskRussia

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