Advertisement

Siberian Mathematical Journal

, Volume 48, Issue 5, pp 939–948 | Cite as

Index sets of decidable models

  • E. B. Fokina
Article

Abstract

We study the index sets of the class of d-decidable structures and of the class of d-decidable countably categorical structures, where d is an arbitrary arithmetical Turing degree. It is proved that the first of them is m-complete ∑ 3 0, d , and the second is m-complete ∑ 3 0, d \∑ 3 0, d in the universal computable numbering of computable structures for the language with one binary predicate.

Keywords

index set computable structure decidable structure countably categorical theory 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Calvert W., “The isomorphism problem for classes of computable fields,” Arch. Math. Logic, 34, No. 3, 327–336 (2004).CrossRefMathSciNetGoogle Scholar
  2. 2.
    Calvert W., “The isomorphism problem for computable Abelian p-groups of bounded length,” J. Symbolic Logic, 70, No. 1, 331–345 (2005).MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Calvert W., Cummins D., Knight J. F., and Miller S., “Comparing classes of finite structures, ” Algebra and Logic, 43, No. 6, 374–392 (2004).CrossRefMathSciNetGoogle Scholar
  4. 4.
    Calvert W., Harizanov V., Knight J. F., and Miller S., “Index sets of computable structures, ” Algebra and Logic, 45, No. 5, 306–325 (2006).CrossRefMathSciNetGoogle Scholar
  5. 5.
    Csima B. F., Montalbán A., and Shore R. A., “Boolean algebras, Tarski invariants, and index sets,” Notre Dame J. Formal Logic, 47, No. 1, 1–23 (2006).MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Dobritsa V. P., “Complexity of the index set of a constructive model,” Algebra and Logic, 22, No. 4, 269–276 (1983).CrossRefMathSciNetGoogle Scholar
  7. 7.
    Goncharov S. S. and Knight J. F., “Computable structure and non-structure theorems,” Algebra and Logic, 41, No. 6, 351–373 (2002).CrossRefMathSciNetGoogle Scholar
  8. 8.
    Lempp S. and Slaman T., “The complexity of the index sets of ℵ0-categorical theories and of Ehrenfeucht theories,” in: Advances in Logic (North Texas Logic Conference), Amer. Math. Soc., Providence RI, 2007, pp. 43–47.Google Scholar
  9. 9.
    White W., “On the complexity of categoricity in computable structures,” Math. Logic Quart., 49, No. 6, 603–614 (2003).MATHCrossRefGoogle Scholar
  10. 10.
    White W., Characterizations for Computable Structures, PhD dissertation, Cornell Univ. (2000).Google Scholar
  11. 11.
    Goncharov S. S. and Khoussainov B., “Complexity of theories of computable categorical models, ” Algebra and Logic, 43, No. 6, 365–373 (2004).CrossRefMathSciNetGoogle Scholar
  12. 12.
    Goncharov S. S., “The problem of the number of nonautoequivalent constructivizations,” Algebra and Logic, 19, No. 6, 401–414 (1980).MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Goncharov S. S., “Computability and computable models, mathematical problems from applied logic. II,” in: Logics for the XXIst Century. Edited by D. M. Gabbay, S. S. Goncharov, and M. Zakharyaschev, Springer-Verlag, New York, 2006, pp. 99–216 (International Mathematical Series, New York).Google Scholar
  14. 14.
    Marker D., “Non-Σn-axiomatizable almost strongly minimal theories,” J. Symbolic Logic, 54, No. 3, 921–927 (1989).MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Ershov Yu. L., Theory of Numberings. 3 [in Russian], Novosibirsk Univ., Novosibirsk (1974).Google Scholar
  16. 16.
    Rogers H., Theory of Recursive Functions and Effective Computability, McGraw-Hill, New York etc. (1967).MATHGoogle Scholar
  17. 17.
    Schmerl J. H., “A decidable ℵ0-categorical theory with a nonrecursive Ryll-Nardzewski function,” Fund. Math., 98, No. 2, 121–125 (1978).MATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia

Personalised recommendations