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Existential equivalence of ordered abelian groups with parameters

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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-subgroupG 0. We determine whetherG andH are existentially equivalent overG 0. 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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  1. Fakultät für Mathematik und Informatik, Universität Passau, Innstrasse 33, D-8390, Passau, Federal Republic of Germany

    V. Weispfenning

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  1. V. Weispfenning
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Weispfenning, V. Existential equivalence of ordered abelian groups with parameters. Arch Math Logic 29, 237–248 (1990). https://doi.org/10.1007/BF01651327

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  • DOI: https://doi.org/10.1007/BF01651327

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