Minor fix

Signed-off-by: zeramorphic <[email protected]>

iii/forcing/02_constructibility.tex

@@ -412,12 +412,12 @@ \subsection{Well-ordering the universe}
         \item \( <_{\alpha + 1}^0 \) is the well-ordering of \( \mathrm{L}_\alpha \cup \qty{\mathrm{L}_\alpha} \) given by making \( \qty{\mathrm{L}_\alpha} \) the maximal element.
         \item Suppose that \( <_{\alpha + 1}^n \) is defined.
         We end-extend \( <_{\alpha + 1}^n \) to form \( <_{\alpha + 1}^{n + 1} \) as follows.
-        Suppose \( x, y \notin \mathcal D^n(\mathrm{L}_\alpha) \).
+        Suppose \( x, y \notin \mathcal D^n(\mathrm{L}_\alpha \cup \qty{\mathrm{L}_\alpha}) \).
         We say \( x <_{\alpha + 1}^{n+1} \) if either
         \begin{enumerate}
-            \item the least \( i \leq 10 \) such that \( \exists u, v \in \mathcal D^n(\mathrm{L}_\alpha) \) with \( x = \mathcal F_i(u, v) \) is less than the least \( i \leq 10 \) such that \( \exists u, v \in \mathcal D^n(\mathrm{L}_\alpha) \) with \( \mathcal y = \mathcal F_i(u, v) \); or
-            \item these indices \( i \) are equal, and the \( <_{\alpha + 1}^n \)-least \( u \in \mathcal D^n(\mathrm{L}_\alpha) \) such that there exists \( v \in \mathcal D^n(\mathrm{L}_\alpha) \) with \( x = \mathcal F_i(u, v) \) is less than the \( <_{\alpha + 1}^n \)-least \( u \in \mathcal D^n(\mathrm{L}_\alpha) \) such that there exists \( v \in \mathcal D^n(\mathrm{L}_\alpha) \) with \( y = \mathcal F_i(u, v) \); or
-            \item both of these coincide, and \( <_{\alpha + 1}^n \)-least \( v \in \mathcal D^n(\mathrm{L}_\alpha) \) with \( x = \mathcal F_i(u, v) \) is less than the least \( v \in \mathcal D^n(\mathrm{L}_\alpha) \) with \( y = \mathcal F_i(u, v) \).
+            \item the least \( i \leq 10 \) such that \( \exists u, v \in \mathcal D^n(\mathrm{L}_\alpha \cup \qty{\mathrm{L}_\alpha}) \) with \( x = \mathcal F_i(u, v) \) is less than the least \( i \leq 10 \) such that \( \exists u, v \in \mathcal D^n(\mathrm{L}_\alpha \cup \qty{\mathrm{L}_\alpha}) \) with \( \mathcal y = \mathcal F_i(u, v) \); or
+            \item these indices \( i \) are equal, and the \( <_{\alpha + 1}^n \)-least \( u \in \mathcal D^n(\mathrm{L}_\alpha \cup \qty{\mathrm{L}_\alpha}) \) such that there exists \( v \in \mathcal D^n(\mathrm{L}_\alpha \cup \qty{\mathrm{L}_\alpha}) \) with \( x = \mathcal F_i(u, v) \) is less than the \( <_{\alpha + 1}^n \)-least \( u \in \mathcal D^n(\mathrm{L}_\alpha \cup \qty{\mathrm{L}_\alpha}) \) such that there exists \( v \in \mathcal D^n(\mathrm{L}_\alpha \cup \qty{\mathrm{L}_\alpha}) \) with \( y = \mathcal F_i(u, v) \); or
+            \item both of these coincide, and \( <_{\alpha + 1}^n \)-least \( v \in \mathcal D^n(\mathrm{L}_\alpha \cup \qty{\mathrm{L}_\alpha}) \) with \( x = \mathcal F_i(u, v) \) is less than the least \( v \in \mathcal D^n(\mathrm{L}_\alpha \cup \qty{\mathrm{L}_\alpha}) \) with \( y = \mathcal F_i(u, v) \).
         \end{enumerate}
     \end{enumerate}
 \end{proof}