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lines changed Original file line number Diff line number Diff line change @@ -152,7 +152,7 @@ \section{Partial Isomorphisms}
152152 $ x_1 $ , \dots ,~$ x_n$ , then $ \Sat {M}{!A}[s_1 ]$ if and
153153 only if~$ \Sat {N}{!A}[s_2 ]$ .
154154 \item $ I_{n+1} (\mathbf {a},\mathbf {b})$ if and only if for every
155- $ a\in A $ there is a $ b\in B $ such that $ I_n
155+ $ a\in \Domain M $ there is a $ b\in \Domain N $ such that $ I_n
156156 (\mathbf {a}a,\mathbf {b}b)$ , and vice-versa.
157157 \end {enumerate }
158158\end {defn }
@@ -198,7 +198,7 @@ \section{Partial Isomorphisms}
198198
199199 Given $ a \in \Domain M$ , let $ !T^a_n$ be set of !!{formula}s
200200 $ !B(x,\mathbf {y})$ of rank no greater than $ n$ satisfied by
201- $ \mathbf {a}a$ in $ \Struct {M}$ ; $ \tau ^a_n$ is finite, so we can
201+ $ \mathbf {a}a$ in $ \Struct {M}$ ; $ !T ^a_n$ is finite, so we can
202202 assume it is a single first-order !!{formula}. It follows that
203203 $ \mathbf {a}$ satisfies $ \lexists [x][!T^a_n(x,\mathbf {y})]$ , which
204204 has quantifier rank no greater than $ n+1 $ . By hypothesis
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