For every logic \(\bL\) and every \(\bL\)-theory \(T\) the relation \(\bOmega^{\sim}_{\bFm_L }(T)\) defined in this way is the greatest congruence compatible with all the \(\bL\)-theories that extend \(T\). Therefore, it holds that \[\bOmega^{\sim}_{\bFm_L }(T) = \bigcap_{T' \in \tTH(\bL)^T} \bOmega_{\bFm_L }(T'),\] where \(\tTH(\bL)^T = \{T' \in \tTH(\bL): T \subseteq T'\}\). The relation \(\bOmega^{\sim}_{\bFm_L }(T)\) is known as the Suszko congruence of \(T\) (w.r.t. \(\bL)\). Suszko defined it —in an equivalent way— in 1977.