Studia Logica 108 (2):255-275 (2020)

Abstract
We characterize, in syntactic terms, the ranges of epimorphisms in an arbitrary class of similar first-order structures. This allows us to strengthen a result of Bacsich, as follows: in any prevariety having at most \ non-logical symbols and an axiomatization requiring at most \ variables, if the epimorphisms into structures with at most \ elements are surjective, then so are all of the epimorphisms. Using these facts, we formulate and prove manageable ‘bridge theorems’, matching the surjectivity of all epimorphisms in the algebraic counterpart of a logic \ with suitable infinitary definability properties of \, while not making the standard but awkward assumption that \ comes furnished with a proper class of variables.
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DOI 10.1007/s11225-019-09846-5
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References found in this work BETA

Equivalence of Consequence Operations.W. J. Blok & Bjarni Jónsson - 2006 - Studia Logica 83 (1-3):91-110.
Protoalgebraic Logics.Janusz Czelakowski - 2003 - Studia Logica 74 (1):313-342.
Correspondences Between Gentzen and Hilbert Systems.J. G. Raftery - 2006 - Journal of Symbolic Logic 71 (3):903 - 957.

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