Quasivariety

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 ${\displaystyle s_{1}\approx t_{1}\land \ldots \land s_{n}\approx t_{n}\rightarrow s\approx t}$, where ${\displaystyle s,s_{1},\ldots ,s_{n},t,t_{1},\ldots ,t_{n}}$ are terms built up from variables using the operation symbols of the specified signature.

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