The equational language of relation algebras is highly expressive, and the deductive power of the equational theory is substantial. In fact, every statement about binary relations that can be expressed in the first-order language of relations using at most three variables can equivalently be expressed as an equation in the language of relation algebras, and vice versa. Furthermore, an equation is derivable from the axioms of relation algebras if and only if a corresponding three-variable sentence is provable in a certain restricted version of first-order logic in which there are just three variables.
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