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2023-07-27 18:58:45 -07:00
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@ -7,7 +7,8 @@ This is read \say{$S$ satisfies $\varphi$}
\definition{}
Let $S$ and $T$ be structures. \par
We say $S$ and $T$ are \textit{equivalent} and write $S \equiv T$ if for any formula $\varphi$, $S \models \varphi \Longleftrightarrow T \models \varphi$.
We say $S$ and $T$ are \textit{equivalent} and write $S \equiv T$ if for any formula $\varphi$, $S \models \varphi \Longleftrightarrow T \models \varphi$. \par
If $S$ and $T$ are not equivalent, we write $S \not\equiv T$.
\problem{}
Show that $