\begin{definition}[Definition:Elementary Equivalence]
Let $\MM, \NN$ be $\LL$-structures.
We say that $\MM$ and $\NN$ are '''elementarily equivalent''' if for all $\LL$-sentences $\phi$, we have $\MM \models \phi$ {{iff}} $\NN \models \phi$.
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Category:Definitions/Model Theory
\end{definition}