 In the last section, we saw that to provide a logic with an algebraic semantics we need in many cases to consider in every algebra a set of designated elements instead of a single designated one. In the examples we discussed, the set of designated elements was definable in the algebras by one equation. This motivated the definition of algebraic semantics in  Section 5.  For many logics, to obtain a semantics similar to an algebraic semantics using the class of algebras naturally associated with them one needs for every algebra a set of designated elements that cannot be defined using only the equations of the algebraic language or is not even definable by using this language only. As we already mentioned, one example where this happens is the local consequence of the normal modal logic \(K\). Also, recall that there are logics with no algebraic semantics at all.