Archive for Mathematical Logic

, Volume 29, Issue 4, pp 237–248 | Cite as

Existential equivalence of ordered abelian groups with parameters

  • V. Weispfenning
Article

Summary

In [GK], Gurevich and Kokorin proved that any two non-trivial ordered abelian groups (o-groups, for short) satisfy the same existential sentences. Let nowG, H be non-trivialo-groups with a commono-subgroupG0. We determine whetherG andH are existentially equivalent overG0. As a corollary, we obtain algebraic criteria for deciding, whether ano-subgroupG is existentially closed in ano-groupH. Corresponding results are proved foro-groups in which congruences are regarded as atomic relations.

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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • V. Weispfenning
    • 1
  1. 1.Fakultät für Mathematik und InformatikUniversität PassauPassauFederal Republic of Germany

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