From e12adf55100b5f3a908b77ca5d28a4f971028cd1 Mon Sep 17 00:00:00 2001
From: Tim Button <54142983+timbutton@users.noreply.github.com>
Date: Mon, 10 Nov 2025 15:45:57 +0000
Subject: [PATCH] Update recursion.tex
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Small typo fixed in proof of bounded recursion; to get a γ+ approximation, we add <γ, τ(g)>
---
 content/set-theory/spine/recursion.tex | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/content/set-theory/spine/recursion.tex b/content/set-theory/spine/recursion.tex
index c65da945..708a4535 100644
--- a/content/set-theory/spine/recursion.tex
+++ b/content/set-theory/spine/recursion.tex
@@ -37,7 +37,7 @@
 The empty function is trivially an $\emptyset$-approximation. 
 
 If $g$ is a $\gamma$-approximation, then $g \cup
-\{\tuple{\ordsucc{\gamma}, \tau(g)}\}$ is a $\ordsucc{\gamma}$-approximation.
+\{\tuple{\gamma, \tau(g)}\}$ is a $\ordsucc{\gamma}$-approximation.
 
 If $\gamma$ is a limit ordinal and $g_\delta$ is a $\delta$-approximation for all $\delta < \gamma$, let $g = \bigcup_{\delta \in \gamma} g_\delta$. This
 is a function, since our various $g_\delta$s agree on all values. And
@@ -127,4 +127,5 @@
 Now, to vindicate \olref[valpha]{defValphas}, just take $A
 = \emptyset$ and $\tau(x) = \Pow{x}$ and $\theta(x) = \bigcup x$. At long last, this vindicates the definition of the $V_\alpha$s!{}
 
-\end{document}
\ No newline at end of file
+
+\end{document}