Model

An interpretation (a domain together with assignments for the nonlogical symbols of a language) that makes a particular formula, set of formulas, or an entire theory true; commonly described as a structure that satisfies those sentences.

A mathematical structure that assigns meanings to the symbols of a formal language (a signature)—a domain together with interpretations of constants, functions, and relations—such that sentences of the language can be evaluated as true or false in that structure.

A mathematical structure consisting of a domain together with interpretations of the symbols of a formal signature (constants, functions, relations) that makes each sentence of a given theory true in that structure.