Existential equivalence of ordered abelian groups with parameters

Archive for Mathematical Logic 29 (4):237-248 (1990)

Abstract
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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DOI 10.1007/BF01651327
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On the Elementary Theory of Hensel Fields.Volker Weispfenning - 1976 - Annals of Pure and Applied Logic 10 (1):59.

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