 The concept of algebraizable logic introduced by Blok and Pigozzi, which we will discuss in  Section 9,  can be described roughly by saying that a logic \(\bL\) is algebraizable if it has an algebraic semantics \((\bK, \iEq)\) such that (1) \(\bK\) is included in the natural class of algebras \(\bAlg^*\bL\) associated with \(\bL\) and (2) the fact that \((\bK, \iEq)\) is an algebraic semantics can be proved by using the Lindenbaum-Tarski method slightly generalized.