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content/incompleteness/introduction/definitions.tex
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\end{defn}
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$\Th{TA}$ is a theory, for whenever $\Th{TA} \Entails !A$, $!A$ is
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-satisfied in every !!{structure} which satisfies $\Th{TA}$. Since
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-$\Sat{M}{\Th{TA}}$, $\Sat{M}{!A}$, and so $!A \in \Th{TA}$.
+satisfied in every !!{structure} which satisfies~$\Th{TA}$. Since
+$\Sat{N}{\Th{TA}}$, we have that~$\Sat{N}{!A}$, and so $!A \in \Th{TA}$.
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The other way to specify a theory~$\Gamma$ is as the set of
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!!{sentence}s entailed by some set of sentences~$\Gamma_0$. In that
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