Model - Dr. A's Wiki

Propositional Logic:

In terms of a logic formula, a ["Model"] is some assignment of variables that causes the formula to be true.

First Order Logic:

A model for a set $X$ of formulas is an interpretation $M$ for $X$ such that every formula of $X$ is true in $M$ .

A domain $D$ is any nonempty set. An interpretation for a set of formulas $X$ , is a domain $D$ together with a rule that

assigns to each $n$ -place predicate symbol (that occurs in a formula) of $X$ an $n$ -place predicate in $D$ ;
assigns to each $n$ -place operation symbol of $X$ an $n$ -place operation in $D$ ;
assigns to each constant symbol of $X$ an element of $D$ ; and
assigns to $=$ the identity predicate $=$ in $D$ , defined by: $a = b$ iff $a$ and $b$ are the same.

See: First Order Mathematical Logic by Angelo Margaris p 145