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Algebraic Characterizations of Various Beth Definability Properties

Eva Hoogland
Studia Logica: An International Journal for Symbolic Logic
Vol. 65, No. 1, Abstract Algebraic Logic I (Jun., 2000), pp. 91-112
Published by: Springer
Stable URL: http://www.jstor.org/stable/20000242
Page Count: 22
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Algebraic Characterizations of Various Beth Definability Properties
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Abstract

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 [20]. Finally, the characterization of the projective Beth property for varieties of modal algebras by L. Maksimova (see [15]) will be shown to hold for the larger class of semantically algebraizable logics.

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