In this paper, we generalize the omitting types theorem, an important result of classical model theory, for a wide class of fuzzy logics, containing the prominent logics of left-continuous t-norms and uninorms.

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In this paper we investigate the Hennessy-Milner property for models of many-valued modal logics defined based on complete MTL-chains having many-valued accessibility relations. Our main result gives a necessary and sufficient algebraic condition for the class of image-finite models for such modal logics to admit the Hennessy-Milner property.

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