Archive for Mathematical Logic

, Volume 29, Issue 4, pp 237–248

Existential equivalence of ordered abelian groups with parameters

  • V. Weispfenning

DOI: 10.1007/BF01651327

Cite this article as:
Weispfenning, V. Arch Math Logic (1990) 29: 237. doi:10.1007/BF01651327


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.

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

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