The equational theory of union-free algebras of relations

We solve a problem of Jónsson 12] by showing that the class of (isomorphs of) algebras of binary relations, under the operations of relative product, conversion, and intersection, and with the identity element as a distinguished constant, is not axiomatizable by a set of equations. We also show that the set of equations valid in is decidable, and in fact the set of equations true in the class of all positive algebras of relations is decidable.Presented by B. M. Schein.H. Andréka's research was supported by Hungarian National Research Fund No. 1911 and No. 2258.