Equivalential and algebraizable logics

Studia Logica 57 (2-3):419 - 436 (1996)
Abstract
The notion of an algebraizable logic in the sense of Blok and Pigozzi [3] is generalized to that of a possibly infinitely algebraizable, for short, p.i.-algebraizable logic by admitting infinite sets of equivalence formulas and defining equations. An example of the new class is given. Many ideas of this paper have been present in [3] and [4]. By a consequent matrix semantics approach the theory of algebraizable and p.i.-algebraizable logics is developed in a different way. It is related to the theory of equivalential logics in the sense of Prucnal and Wroski [18], and it is extended to nonfinitary logics. The main result states that a logic is algebraizable (p.i.-algebraizable) iff it is finitely equivalential (equivalential) and the truth predicate in the reduced matrix models is equationally definable.
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    J. Czelakowski & D. Pigozzi (2004). Fregean Logics. Annals of Pure and Applied Logic 127 (1-3):17-76.
    James G. Raftery (2013). Order algebraizable logics. Annals of Pure and Applied Logic 164 (3):251-283.
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