 We shall now discuss the two definitions that have been considered as providing natural classes of algebras associated with a logic \(\bL\). Both definitions can be seen as arising from an abstraction of the Lindenbaum-Tarski method and we follow this path in introducing them. The common feature of these abstractions is that in them the specific way in which the relation \(\theta(T)\) is defined in the Lindenbaum-Tarski method is disregarded.