Algebraic Characterizations of Various Beth Definability Properties
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- Hoogland, E. Studia Logica (2000) 65: 91. doi:10.1023/A:1005295109904
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In this paper it will be shown that the Beth definability property corresponds to surjectiveness of epimorphisms in abstract algebraic logic. This generalizes a result by I. Németi (cf. [11, Theorem 5.6.10]). Moreover, an equally general characterization of the weak Beth property will be given. This gives a solution to Problem 14 in . Finally, the characterization of the projective Beth property for varieties of modal algebras by L. Maksimova (see ) will be shown to hold for the larger class of semantically algebraizable logics.