On quasi-identities of relation algebras with Diophantine operations (Q1363476)

Let \(\operatorname{Rel}(U)\) denote the set of all binary relations defined on a set \(U\). Consider the set of operations \(F_{\varphi}(r_{1}, \ldots, r_{n}) = (x, y)\), where \(\varphi(x, y, r_{1}, \ldots, r_{n})\) is valid in \(U\) on elements \(x, y\) and relations \(r_{1}, \ldots, r_{n}\). A set of relations \(\Phi \subseteq \operatorname{Rel}(U)\) closed under a set \(\Omega\) of operations defines the relation algebra \((\Phi, \Omega )\). A relation algebra is Diophantine if all its operations are Diophantine (= primitive-positive). Classes of Diophantine relation algebras are studied in the article. Quasi-equational theories of the classes are described and bases of quasi-identities are constructed.