 Conditions  (1)  and  (2)  of the definition of algebraizable logic (instantiated to \(\bAlg^*\bL\)) encode the fact that there is a very strong link between an algebraizable logic \(\bL\) and its class of algebras \(\bAlg\bL\), so that this class of algebras reflects the metalogical properties of \(\bL\) by algebraic properties of \(\bAlg\bL\) and conversely.