  The general aim of this article is to study the negation fragment of
classical logic within the framework of contemporary (Abstract) Algebraic
Logic. More precisely, we shall find the three classes of algebras that are
canonically associated with a logic in Algebraic Logic, that is, we find the
classes $\mathrm{Alg}^*$, $\mathrm{Alg}$ and the intrinsic variety of the
negation fragment of classical logic. In order to achieve this, firstly we
propose a Hilbert-style axiomatization for this fragment. Then, we characterize
the reduced matrix models and the full generalized matrix models of this logic.
Also, we classify the negation fragment in the Leibniz and Frege hierarchies.
