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A structure supplies a nonempty domain and an interpretation of every constant, operation, and relation symbol in its language.

This is a structure for a first-order language, with finitary interpretations of its nonlogical symbols.

A structure consists of a domain together with interpretations of the symbols of a formal language. In the usual finitary setting it interprets constant, function, and relation symbols of their declared arities. A first-order structure is such an interpretation for first-order logic.