A single quasi-identity for a quasivariety with the Fraser-Horn property (Q1185227)

A quasivariety \(\mathbb{K}\) is said to be finitely axiomatizable relative to \(H(\mathbb{K})\) if there exists a finite set \(\Sigma\) of quasi-identities such that for all \(A\) of \(H(\mathbb{K})\), \(A\in\mathbb{K}\) iff \(A\) satisfies each quasi- identity of \(\Sigma\) (or equivalently, \(\mathbb{K}=\text{Mod(Id}(\mathbb{K})\cup\Sigma)\), where \(\text{Id}(\mathbb{K})\) denotes the set of identities of \(\mathbb{K})\). The main goal of the authors to prove: Theorem 3. Let \(\mathbb{K}\) be a quasi-variety of algebras with Fraser-Horn property that is finitely axiomatizable relative to \(H(\mathbb{K})\). Then \(\mathbb{K}\) can be axiomatized relative to \(H(\mathbb{K})\) by a single quasi- identity. --- The authors prove some interesting corollaries as well.