We prove that, if V is an effectively given commutative valuation domain such that its value group is dense and archimedean, then the theory of all V -modules is decidable.
Abstract. We will develop the model theory of modules over commutative Bézout domains. In particular we characterize commutative Bézout domains B whose lattice of pp-formulae has no width and give some applications to the existence of superdecomposable pure injective B-modules.
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