# Definition:Theory (Logic)/Structure

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## Definition

Let $\LL$ be a logical language.

Let $\MM$ be an $\LL$-structure.

The **$\LL$-theory of $\MM$** is the $\LL$-theory consisting of those $\LL$-sentences $\phi$ such that:

- $\MM \models \phi$

where $\models$ denotes that $\MM$ is a model for $\phi$.

This theory can be denoted $\map {\operatorname{Th} } \MM$ when the language $\LL$ is understood.

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