Siberian Mathematical Journal

, Volume 46, Issue 3, pp 405–412 | Cite as

On Automorphic Tuples of Elements in Computable Models

  • S. S. Goncharov
  • V. S. Harizanov
  • J. F. Knight
  • A. S. Morozov
  • A. V. Romina


A criterion is obtained for existence of two isomorphic but not hyperarithmetically isomorphic tuples in a hyperarithmetical model. This criterion is used to show that such a situation occurs in the models of well-known classes.


model computability computable model hyperarithmetical model automorphism recursive automorphism admissible sets recursive model constructive model Scott rank quantifier rank automorphic tuples 


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  1. 1.
    Barwise J., Admissible Sets and Structures, Springer-Verlag, Berlin (1975).Google Scholar
  2. 2.
    Ash C. J. and Knight J. F., Computable Structures and the Hyperarithmetical Hierarchy, Elsevier, Amsterdam (2000).Google Scholar
  3. 3.
    Ershov Yu. L. and Goncharov S. S., Constructive Models (Siberian School of Algebra and Logic), Kluwer Academic/Plenum Publishers, New York (2000).Google Scholar
  4. 4.
    Morozov A. S., “Functional trees and automorphisms of models,” Algebra and Logic, 32, No.1, 28–38 (1993).Google Scholar
  5. 5.
    Harrison J., “Recursive pseudo-well-ordering,” Trans. Amer. Math. Soc., 131, 526–543 (1968).Google Scholar
  6. 6.
    Barwise J. and Moschovakis Y. N., “Global inductive definability,” J. Symbolic Logic, 43, No.3, 521–534 (1978).Google Scholar
  7. 7.
    Sacks G. E., Higher Recursion Theory, Springer-Verlag, Heidelberg (1990).Google Scholar
  8. 8.
    Rogers L., “The structure of p-trees: algebraic systems related to Abelian groups,” in: Abelian Group Theory. Proc. Second New Mexico State Univ. Conf. Las Cruces, N.M., 1976, Springer-Verlag, Berlin, 1977, pp. 57–72. (Lecture Notes in Math.; 616.)Google Scholar
  9. 9.
    Rogers H., Theory of Recursive Functions and Effective Computability, McGraw-Hill Book Company, New York; St. Louis; San Francisco; Toronto; London; Sydney (1967).Google Scholar
  10. 10.
    Fuchs L., Infinite Abelian Groups. Vol. 1, Academic Press, New York (1970).Google Scholar
  11. 11.
    Alaev P. E., “Scott ranks of Boolean algebras,” in: Trudy Inst. Mat. (Novosibirsk), 1996, 30, pp. 3–25.Google Scholar
  12. 12.
    Goncharov S. S., “Constructivizability of superatomic Boolean algebras,” Algebra and Logic, 12, No.1, 17–22 (1973).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • S. S. Goncharov
    • 1
  • V. S. Harizanov
    • 2
  • J. F. Knight
    • 3
  • A. S. Morozov
    • 1
  • A. V. Romina
    • 4
  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.George Washington UniversityWashingtonUSA
  3. 3.University of Notre DameNotre Dame
  4. 4.Max-Planck Institut fur InformatikSaarbruckenGermany

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