Geodesic
Finiteness Conditions for Algebras of Relations
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical logic and algebra, Tome 242 (2003), pp. 103-107.

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Algebras of relations on a given set are considered; operations in an algebra are specified by various formulas of first-order logic. Different ways of introducing finiteness conditions for such algebras are studied. For each natural $n$, an example of an algebra is constructed that is generated by one $n$-ary relation and cannot be generated by its relations of smaller arity. An open problem is formulated. 
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A. L. Semenov. Finiteness Conditions for Algebras of Relations. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical logic and algebra, Tome 242 (2003), pp. 103-107. http://geodesic.mathdoc.fr/item/TM_2003_242_a7/

[1] Semenov A. L., “Ob opredelimosti arifmetiki v ee fragmentakh”, DAN SSSR, 263:1 (1982), 44–47 | MR | Zbl

[2] Semenov A. L., “Logicheskie teorii odnomestnykh funktsii na naturalnom ryade”, Izv. AN SSSR. Ser. mat., 47:3 (1983), 623–658 | MR