Model - Dr. A 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 of formulas is an interpretation for such that every formula of is true in .

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

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

See: First Order Mathematical Logic by Angelo Margaris p 145