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Josia Pietsch 2024-01-24 16:06:42 +01:00
parent acb56df1c2
commit e59e97ca03
Signed by: josia
GPG key ID: E70B571D66986A2D
2 changed files with 5 additions and 3 deletions

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@ -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.

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@ -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 $A^{<\N}$