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We give a characterization of Σ-cotorsion modules over valuation domains in terms of descending chain conditions on certain chains of definable subgroups. We prove that pure submodules, direct products and modules elementarily equivalent to a Σ-cotorsion module are again Σ-cotorsion. Moreover, we describe the structure of Σ-cotorsion modules.doi:10.1515/forum.2009.044 fatcat:x2gy2y224za4vajkhbrfysqq4m