= First-order variable assignment
{title2=$v:\mathrm{Var}\to A$}
For a <first-order structure> with domain $A$, an assignment maps every individual variable to an element of $A$. It extends recursively to <first-order terms> using the interpreted functions. To evaluate $\forall x\varphi$, vary only the value of $x$ over $A$, holding the other values fixed. The <truth value> of a <first-order formula> depends only on its <free variables>; a <first-order sentence> is therefore independent of the assignment.
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