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. K is a pseudoelementary class closed under subalgebras and direct products.
2. K is the class of all models of a set of quasiidentities, that is, implications of the form , where are terms built up from variables using the operation symbols of the specified signature.