Abstract
We solve a problem of Jonsson [12] by showing that the class ℛ 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 ℛ is decidable, and in fact the set of equations true in the class of all positive algebras of relations is decidable.
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