fix

inputs/lecture_12.tex

@@ -59,12 +59,11 @@
                 Take $A \in \Sigma^1_1(X) \setminus \cB(X)$%
                 \footnote{e.g.~\yaref{thm:universals11}}
                 and $f\colon X \to  Y$ Borel.
-                But then we get that $f^{-1}(B)$ is Borel $\lightnig$.
+                But then we get that $f^{-1}(B)$ is Borel $\lightning$.
             }{.}
     \end{itemize}
 \end{observe}
 
-% TODO ANKI-MARKER
 \begin{theorem}
     \label{thm:lec12:1}
     Suppose that $A \subseteq \cN$ is analytic.

inputs/lecture_13.tex

@@ -1,11 +1,12 @@
 \lecture{13}{2023-11-08}{}
-
+\gist{%
 % Recap
 $\LO = \{x \in 2^{\N\times \N} : x \text{ is a linear order}\} $.
 $\LO \subseteq 2^{\N \times \N}$ is closed
 and $\WO = \{x \in  \LO: x \text{ is a wellordering}\} $
  is coanalytic in $\LO$.
 % End Recap
+}{}
 
 Another way to code linear orders:
 
@@ -32,6 +33,8 @@ with $(f^{-1}(\{1\}), <)$.
     and  $[\alpha_i, \alpha_{i+1})$ to $(i,i+1)$.
 \end{proof}
 
+% TODO ANKI-MARKER
+
 \begin{definition}[\vocab{Kleene-Brouwer ordering}]
     Let $(A,<)$ be a linear order and $A$ countable.
     We define the linear order $<_{KB}$ on $A^{<\N}$