In mathematics, a quasivariety is a class of algebraic structures generalizing the notion of variety by allowing equational conditions on the axioms defining the class.
A trivial algebra contains just one element.
A quasivariety is a class K of algebras with a specified signature satisfying any of the following equivalent conditions:[1] Every variety is a quasivariety by virtue of an equation being a quasi-identity for which n = 0.
The cancellative semigroups form a quasivariety.
Then the class of orderable algebras from K forms a quasivariety, since the preservation-of-order axioms are Horn clauses.