Magidor-Malitz quantifiers in modules

Journal of Symbolic Logic 49 (1):1-8 (1984)
Abstract
We prove the elimination of Magidor-Malitz quantifiers for R-modules relative to certain Q 2 α -core sentences and positive primitive formulas. For complete extensions of the elementary theory of R-modules it follows that all Ramsey quantifiers (ℵ 0 -interpretation) are eliminable. By a result of Baldwin and Kueker [1] this implies that there is no R-module having the finite cover property
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DOI 10.2307/2274085
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