= Substructure of a first-order structure
{title2=$A\subseteq B$}
= Substructures of a first-order structure
{synonym}
An $L$-<substructure of a first-order structure> $A\subseteq B$ has a nonempty domain containing all named constants and closed under the <functions> of $B$, and each relation of $A$ is the restriction of the corresponding relation of $B$. Consequently every <quantifier-free formula> with parameters in $A$ has the same truth value in $A$ and $B$. This is weaker than being an <elementary substructure>, which preserves all <first-order formulas>.
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