Quasi-identity

Summary

A quasi-identity is a law of the form "if these finitely many equations between terms hold, then this further equation holds". It is required for all values of the variables. It generalizes an identity, which is the case with no hypotheses. Quasi-identities are exactly the axioms of quasivarieties, just as identities are the axioms of varieties. They are the strict universal Horn clauses of an algebraic language.