I've read numerous ressources about algebraic logic and the Lindenbaum-Tarski process for prop. logic, but I'm still unclear of how the link to the class of Boolean algebras comes to life.
In he process we create a quotient algebra through a selected theory. The canonical projection with respect to this quotient the provides a suitable homomorphism for the contraposition in the second part of the completeness proof.
How is it however inferred from this one constructed quotient that the prop. calculus is complete with respect to all boolean algebras. Is it from the fact that every theory generates another projection such that the quotients turn out to be isomorphic to the class of Boolean algebras?