Existential equivalence of ordered abelian groups with parameters
- 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.