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}