Algebraic Characterizations of Various Beth Definability Properties
Eva Hoogland

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.~N\'emeti.
Moreover, an equally general characterization of the weak Beth property
will be given. This gives a solution to Problem 14 in \cite{sain:90}.
Finally, the characterization of the projective Beth property for
varieties of modal algebras by L.\ Maksimova will be shown to hold for 
the larger class of semantically algebraizable logics.