Definition:Model (Predicate Logic)

Definition
Let $\mathcal P$ be the predicate symbols of a vocabulary of predicate calculus.

A model for predicate logic of type $\mathcal P$ is a system $\mathcal M$ consisting of:
 * A non-empty set $M$ called the universe of the model $\mathcal M$;
 * A function which assigns an $n$-ary relation $q^{\mathcal M}$ to each $n$-ary predicate symbol $q$ of $\mathcal P$.

Only the universe set $M$ is required to be non-empty. A unary relation $p^{\mathcal M}$ may be any subset of $M$ at all, which includes either empty or not.

Such a model is called a model for predicate calculus or a model for predicate logic.