Algebraic Characterizations of Various Beth Definability Properties
Eva Hoogland

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.