Theories of modules closed under direct products

Journal of Symbolic Logic 57 (2):515-521 (1992)
We generalize to theories of modules (complete or not) a result of U. Felgner stating that a complete theory of abelian groups is a Horn theory if and only if it is closed under products. To prove this we show that a reduced product of modules $\Pi_F M_i (i \in I)$ is elementarily equivalent to a direct product of ultraproducts of the modules $M_i (i \in I)$
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DOI 10.2307/2275285
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Fred Galvin (1970). Horn Sentences. Annals of Mathematical Logic 1 (4):389-422.

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