Decidability of the theory of modules over Prüfer domains with dense value groups

Annals of Pure and Applied Logic 170 (12):102719 (2019)
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Abstract

We provide algebraic conditions ensuring the decidability of the theory of modules over effectively given Prüfer (in particular Bézout) domains whose localizations at maximal ideals have dense value groups. For Bézout domains, these conditions are also necessary.

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References found in this work

Model theory of modules.Martin Ziegler - 1984 - Annals of Pure and Applied Logic 26 (2):149-213.
Decidability for theories of modules over valuation domains.Lorna Gregory - 2015 - Journal of Symbolic Logic 80 (2):684-711.
Model theory of modules over a serial ring.Paul C. Eklof & Ivo Herzog - 1995 - Annals of Pure and Applied Logic 72 (2):145-176.

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