 Blok and Pigozzi’s definition of algebraizable logic in Blok &amp; Pigozzi 1989 was given only for finitary logics and, moreover, they imposed that the sets of defining equations and of equivalence formulas should be finite. Today we say that an algebraizable logic is finitely algebraizable if the sets of equivalence formulas \(\Delta\) and of defining equations \(\iEq\) can both be taken finite. And we say that a logic is Blok-Pigozzi algebraizable (BP-algebraizable) if it is finitary and finitely algebraizable.