= Solution
The assertion that $\mathcal A$ is a <first-order model> of $\Gamma$ means that every <first-order sentence> belonging to $\Gamma$ is true in the <first-order structure>:
$$
\boxed{\mathcal A\models\Gamma\quad\Longleftrightarrow\quad (\forall\gamma\in\Gamma)\ \mathcal A\models\gamma.}
$$
Equivalently each <first-order sentence> is true under every <assignment in a first-order structure>, since <first-order sentences> have no <free variables>. The <first-order sentences> must all hold in the same interpretation of the language; one cannot select a different <first-order structure> for each member of $\Gamma$.
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