 This definition has an equivalent in terms of the closed sets of \(C\): an abstract logic \(\cA = \langle \bA, C \rangle\) is a model of \(\bL\) if and only if for every \(C\)-closed set \(X\) the matrix \(\langle \bA, X \rangle\) is a model of \(\bL\) (i.e., \(X\) is an \(\bL\)-filter).