 Theorem 5.  A logic \(\bL\) is algebraizable if and only if on the algebra of formulas \(\bFm_L\), the map that sends every theory \(T\) to its Leibniz congruence commutes with the inverses of homomorphisms from \(\bFm_L\) to \(\bFm_L\) and it is an isomorphism between the set \(\tTH(\bL)\) of theories of \(\bL\), ordered by inclusion, and the set of congruences \(\theta\) of \(\bFm_L\) such that \(\bFm_L /\theta \in \bAlg\bL\), also ordered by inclusion.