Characterizing equivalential and algebraizable logics by the Leibniz operator (Q1357379)

In this paper the author characterizes the hierarchy of protoalgebraic, equivalential, finitely equivalential, possibly infinitely algebraizable and finitely algebraizable logics by properties of the Leibniz operator. The author gives a new short proof of the main result of \textit{W. J. Blok} and \textit{D. Pigozzi} [Algebraizable logics, Mem. Am. Math. Soc. 396 (1989; Zbl 0664.03042)] that a finitary logic is finitely algebraizable iff the Leibniz operator is injective and preserves unions of directed systems. It is generalized to nonfinitary logics.