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Model theory is the branch of mathematical logic which deals with the connection between a formal language and its interpretations, or models.
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Is the existence of substructures satisfying a theory absolute?
Given a first-order structure $\mathfrak{A}$ and a first-order theory $T$ one can ask if
$$
\varphi(\mathfrak{A}, T) := ``\text{there is a substructure } \mathfrak{B} \text{ of } \mathfrak{A} \text{ …