some small changes

inputs/lecture_01.tex

@@ -1,6 +1,6 @@
 \lecture{01}{2023-10-16}{}
-
+\gist{%
-Literature
+\paragraph{Literature}
 
 \begin{itemize}
     \item Schindler, Set theory
@@ -20,6 +20,7 @@ Literature
             \item Independence of $\CH$.
         \end{itemize}
 \end{itemize}
+}{}
 
 
 \section{Naive set theory}

inputs/lecture_10.tex

@@ -6,6 +6,7 @@ Applications of induction and recursion:
     such that $x \in t$.
 \end{fact}
 \begin{proof}
+\gist{%
     Take $R = \in $.
     We want a function $F$ with domain $\omega$
     such that $F(0) = \{x\}$
@@ -27,16 +28,27 @@ Applications of induction and recursion:
      \begin{IEEEeqnarray*}{rCl}
          F(0) &=& \{x\},\\
          F(n+1) &=& \bigcup\bigcup \ran(F\defon{n+1})\\
-                &=& \bigcup \bigcup \{\{x\}, x, \bigcup x, \ldots, \underbrace{\bigcup^{n-1} x}_{F(n)}\}
+                &=& \bigcup \bigcup \{\{x\}, x, \bigcup x, \ldots, \underbrace{\bigcup\nolimits^{n-1} x}_{F(n)}\}
                     = \bigcup F(n),
      \end{IEEEeqnarray*}
      i.e.~$F(n+1) = \bigcup F(n)$.
+}{%
+    \begin{itemize}
+        \item Use recursion ($\in $) to define $F\colon \omega \to V$
+            such that
+            \[
+            F(0) = \{x\}, F(n+1) = \bigcup F(n).
+            \]
+        \item $\{x\} \cup \bigcup \ran(F)$ is as desired.
+    \end{itemize}
+}
 \end{proof}
-
+\gist{%
 \begin{notation}
     Let $\OR$ denote the class of all ordinals
     and $V$ the class of all sets.
 \end{notation}
+}{}
 \begin{lemma}
     There is a function $F\colon \OR \to  V$
     such that $F(\alpha) = \bigcup \{\cP(F(\beta)): \beta < \alpha\}$.
@@ -65,7 +77,7 @@ Applications of induction and recursion:
     \end{enumerate}
 \end{proof}
 \begin{notation}
-    Usually, one write $V_\alpha$ for $F(\alpha)$.
+Usually, one writes $V_\alpha$ for $F(\alpha)$.
     They are called the \vocab{rank initial segments}  of $V$.
 \end{notation}
 \begin{lemma}

inputs/lecture_12.tex

@@ -52,15 +52,23 @@ We will very rarely use ordinal arithmetic.
 \begin{definition}
     Let $\alpha$, $\beta$ be ordinals.
     We say that $f\colon  \alpha \to \beta$ is \vocab{cofinal}
-    iff for all $\xi < \beta$, there is some $\eta < \alpha$
+    iff
-    such that $f(\eta) \ge \xi$.
+    \gist{%
+        for all $\xi < \beta$, there is some $\eta < \alpha$
+        such that $f(\eta) \ge \xi$.%
+    }{%
+        \[
+        \forall \xi < \beta.~\exists \eta < \alpha.~f(\eta) \ge \xi.
+        \]
+    }
 \end{definition}
+\gist{%
 \begin{remark}
     If $\beta$ is a limit ordinal,
     this is equivalent to
     \[
-    \forall  \xi < \beta .~\exists \eta  \alpha.~f(\eta) > \xi.
+    \forall  \xi < \beta .~\exists \eta  < \alpha.~f(\eta) > \xi.
-    \] 
+    \]
 \end{remark}
 \begin{example}
     \begin{enumerate}[(a)]
@@ -79,7 +87,7 @@ We will very rarely use ordinal arithmetic.
             is cofinal.
     \end{enumerate}
 \end{example}
-
+}{}
 \begin{definition}
     Let $\beta$ be an ordinal.
     The \vocab{cofinality} of $\beta$,
@@ -87,7 +95,7 @@ We will very rarely use ordinal arithmetic.
     is the least ordinal $\alpha$
     such that there exists a cofinal
     $f\colon \alpha \to \beta$.
-\end{definition}k
+\end{definition}
 \begin{example}
     \begin{itemize}
         \item $\cf(\aleph_\omega) = \omega$.
@@ -139,7 +147,7 @@ In particular, a regular ordinal is always a cardinal.
     Clearly this is cofinal.
 \end{proof}
 \begin{warning}
-    Note that in general, a composition of cofinal map
+    Note that in general, a composition of cofinal maps
     is not necessarily cofinal.
 \end{warning}
 

jrpie-gist.sty

@@ -0,0 +1,14 @@
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{jrpie-gist}[2023/01/22 - gist version for lecture notes]
+
+% TODO gist info
+% TODO link to long version (provide link to main document)
+
+% TODO \phantomsection to cross link
+\newcommand{\gist}[2]{%
+    \ifcsname EnableGist\endcsname%
+        #2%
+    \else%
+        #1%
+    \fi%
+}

logic.sty

@@ -9,6 +9,7 @@
 \usepackage{mkessler-code}
 \usepackage{jrpie-math}
 \usepackage{jrpie-yaref}
+\usepackage{jrpie-gist}
 \usepackage[normalem]{ulem}
 \usepackage{pdflscape}
 \usepackage{longtable}
@@ -22,6 +23,7 @@
 \usepackage{listings}
 \usepackage{multirow}
 \usepackage{float}
+\usepackage{scalerel}
 %\usepackage{algorithmicx}
 
 \newcounter{subsubsubsection}[subsubsection]
@@ -107,14 +109,14 @@
 \DeclareSimpleMathOperator{Con}
 
 
-\DeclareMathOperator{\Zermelo}{Z}
+\DeclareMathOperator{\Zermelo}{\mathsf{Z}}
-\DeclareSimpleMathOperator{ZF}
+\DeclareMathOperator{\ZF}{\mathsf{ZF}}
-\DeclareSimpleMathOperator{ZFC}
+\DeclareMathOperator{\ZFC}{\mathsf{ZFC}}
-\DeclareSimpleMathOperator{BG}
+\DeclareMathOperator{\BG}{\mathsf{BG}}
-\DeclareSimpleMathOperator{BGC}
+\DeclareMathOperator{\BGC}{\mathsf{BGC}}
-\DeclareSimpleMathOperator{HOD}
+\DeclareMathOperator{\HOD}{\mathsf{HOD}}
-\DeclareSimpleMathOperator{OD}
+\DeclareMathOperator{\OD}{\mathsf{OD}}
-\DeclareSimpleMathOperator{AC}
+\DeclareMathOperator{\AC}{\mathsf{AC}}
 \newcommand{\AxC}{\yarefs{ax:c}}
 \newcommand{\AxExt}{\yarefs{ax:ext}} % AoE
 \newcommand{\AxFund}{\yarefs{ax:fund}} % AoF
@@ -144,5 +146,5 @@
 
 \newcommand\lecture[3]{\hrule{\color{darkgray}\hfill{\tiny[Lecture #1, #2]}}}
 %\newcommand\diagi{\mathop{\large \Delta}\limits}
-\newcommand\diagi{\mathop{\large \Delta}}
+\newcommand\diagi{\mathop{\scalerel*{\Delta}{\sum}}}
 

logic2-gist.tex

@@ -0,0 +1,2 @@
+\def\EnableGist{}
+\input{logic2}

logic2.tex

@@ -42,11 +42,17 @@
 \input{inputs/lecture_16}
 \input{inputs/lecture_17}
 \input{inputs/lecture_18}
-\input{inputs/lecture_19}
+\gist{
-\input{inputs/lecture_20}
+    \input{inputs/lecture_19}
-\input{inputs/lecture_21}
+    \input{inputs/lecture_20}
-\input{inputs/lecture_22}
+    \input{inputs/lecture_21}
-\input{inputs/lecture_23}
+    \input{inputs/lecture_22}
+    \input{inputs/lecture_23}
+}{
+    \newpage
+    \section{Forcing}
+    The rest of the course is not relevant for the exam.
+}
 
 
 \cleardoublepage