A **finitary relation** in mathematics, particularly in the context of formal logic, set theory, and database theory, refers to a relationship that involves a finite number of elements. More precisely, a relation can be thought of as a subset of a Cartesian product of sets, and when we specify that a relation is finitary, we mean that it is defined for a finite number of tuples.
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A subset of a finite Cartesian product specifies which tuples of elements satisfy a relation. A first-order structure interprets a relation symbol with argument places as such a subset of the -fold Cartesian product of its domain of a first-order structure. For two argument places this is a binary relation; for three, the set of triples satisfying is an example involving addition.