Definition:Assignment for Structure

Definition
Let $\mathcal L_1$ be the language of predicate logic.

Let $\mathrm{VAR}$ be the collection of variables of $\mathcal L_1$.

Let $\mathcal A$ be an $\mathcal L_1$-structure on a set $A$.

An assignment for $\mathcal A$ is a mapping $\sigma$ such that:


 * the codomain of $\sigma$ is $A$
 * the domain of $\sigma$ is a subset of $\mathrm{VAR}$

That is, the domain of $\sigma$ contains only variables, and maps them to elements of $A$.

Also see

 * Definition:Formal Semantics of Structures for Predicate Logic