What causes this difference between \(\bgK\) and \(\blK\) is that the class of reduced matrix models of \(\bgK\) is \[\{\langle \bA, \{1^{\bA }\}\rangle : \bA \in \bMA\},\] but the class of reduced matrix models of \(\blK\) properly includes this class so that for some algebras \(\bA \in \bMA\), in addition to \(\{1^{\bA }\}\) there is some other \(\blK\)-filter \(F\) with \(\langle \bA, F \rangle\) reduced. This fact provides a way to show that \(\blK\) can not be algebraizable by showing that the \(\blK\)-filters of the reduced matrices are not equationally definable from the algebras; if they where, then for every \(\bA \in \bAlg \blK\) there would exist exactly one \(\blK\)-filter \(F\) of \(\bA\) such that \(\langle \bA, F \rangle\) is reduced.