From ef3b65edbd091709448be39e766a2c643c45ab66 Mon Sep 17 00:00:00 2001
From: Josia Pietsch <git@jrpie.de>
Date: Thu, 25 Jan 2024 20:25:21 +0100
Subject: [PATCH] some fix for some problem

---
 inputs/lecture_14.tex | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/inputs/lecture_14.tex b/inputs/lecture_14.tex
index b040edf..258aaca 100644
--- a/inputs/lecture_14.tex
+++ b/inputs/lecture_14.tex
@@ -17,13 +17,13 @@
     \]
     and similarly for $<^\ast$.
     % https://q.uiver.app/#q=WzAsNCxbMCwwLCJZIl0sWzIsMCwiWCJdLFswLDEsIkMnIl0sWzIsMSwiXFxiZWdpbnthcnJheX17Y31DXFxcXFxcUGlfMV4xLVxcdGV4dHtjb21wbGV0ZX1cXGVuZHthcnJheX0iXSxbMCwxLCJmIl0sWzIsMCwiXFxzdWJzZXRlcSIsMCx7InN0eWxlIjp7InRhaWwiOnsibmFtZSI6Imhvb2siLCJzaWRlIjoidG9wIn19fV0sWzMsMSwiXFxzdWJzZXRlcSIsMix7InN0eWxlIjp7InRhaWwiOnsibmFtZSI6Imhvb2siLCJzaWRlIjoidG9wIn19fV1d
-    \begin{tikzcd}
-    	Y && X \\
-    	{C'} && {\begin{array}{c}C\\\Pi_1^1-\text{complete}\end{array}}
-    	\arrow["f", from=1-1, to=1-3]
-    	\arrow["\subseteq", hook, from=2-1, to=1-1]
-    	\arrow["\subseteq"', hook, from=2-3, to=1-3]
-    \end{tikzcd}
+    % \begin{tikzcd}
+    % 	Y && X \\
+    % 	{C'} && {\begin{array}{c}C\\\Pi_1^1-\text{complete}\end{array}}
+    % 	\arrow["f", from=1-1, to=1-3]
+    % 	\arrow["\subseteq", hook, from=2-1, to=1-1]
+    % 	\arrow["\subseteq"', hook, from=2-3, to=1-3]
+    % \end{tikzcd}
     Let $X = 2^{\Q} \supseteq \WO$.
     We have already show that $\WO$ is $\Pi^1_1$-complete.