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Categoricity in Restricted Classes

  • Andrey Morozov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3526)

Abstract

It is well known that only a few structures can be described up to isomorphism by their elementary theories in the class of all models of fixed cardinality. Unfortunately, most of the natural and interesting structures fail to have this property.

References

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    Morozov, A.: On the theories of classes of recursive permutation groups. Siberian Advances in Mathematics 1(1), 138–153 (1991)zbMATHMathSciNetGoogle Scholar
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    Nies, A.: Separating classes of groups by first–order sentences. Internat. J. Algebra Comput. 13, 287–302 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Morozov, A.S., Nies, A.: Finitely generated groups and first order logic. Journal of the London mathematical society (to appear)Google Scholar
  4. 4.
    Tennenbaum, S.: Non-archimedean models for arithmetic. Notices of the American Mathematical Society 6, 270 (1959)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Andrey Morozov
    • 1
  1. 1.Sobolev Institute of MathematicsNovosibirskRussia

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