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Diagram edit
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Signed-off-by: zeramorphic <[email protected]>
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zeramorphic committed Mar 12, 2024
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22 changes: 10 additions & 12 deletions iii/lc/main.tex
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Expand Up @@ -21,7 +21,7 @@ \section{Large large cardinals}
\section*{Diagram of large cardinal properties}
Under suitable consistency assumptions, large cardinal properties that appear in higher positions on this diagram have strictly higher consistency strength than properties appearing lower down the diagram.

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\[\begin{tikzcd}
&&& {\kappa \text{ Reinhardt}} & {0=1} \\
&&& I1 \\
Expand All @@ -30,32 +30,30 @@ \section*{Diagram of large cardinal properties}
&&& {\kappa \text{ strongly compact}} \\
{} & {\smash{\begin{tabular}{c}\text{large}\\\text{medium}\end{tabular}}} &&&&& {} \\
&&& {\kappa \text{ strong}} \\
&&& {\kappa \text{ 2-strong}} \\
&&& {\kappa \text{ surviving}} \\
&& {\kappa \text{ Ulam}} & {\kappa \text{ measurable}} & {\kappa \text{ real-valued measurable}} \\
{} & {\smash{\begin{tabular}{c}\text{medium}\\\text{small}\end{tabular}}} &&&&& {} \\
&&& {\kappa \text{ weakly compact}} \\
&&& {\kappa \text{ inaccessible}} & {\kappa \text{ weakly inaccessible}} \\
&&& {\kappa \text{ worldly}}
\arrow[from=10-4, to=10-5]
\arrow[from=10-5, to=13-5]
\arrow[from=10-4, to=12-4]
\arrow[from=9-4, to=9-5]
\arrow[from=9-5, to=12-5]
\arrow[from=9-4, to=11-4]
\arrow[from=11-4, to=12-4]
\arrow[from=12-4, to=12-5]
\arrow[from=12-4, to=13-4]
\arrow[from=13-4, to=13-5]
\arrow[from=13-4, to=14-4]
\arrow[shift left=2, from=10-4, to=10-3]
\arrow["{\text{min.}}", shift left=2, from=10-3, to=10-4]
\arrow[from=9-4, to=10-4]
\arrow[shift left=2, from=9-4, to=9-3]
\arrow["{\text{min.}}", shift left=2, from=9-3, to=9-4]
\arrow[from=8-4, to=9-4]
\arrow[from=4-4, to=5-4]
\arrow[from=3-4, to=4-4]
\arrow[from=2-4, to=3-4]
\arrow[from=1-4, to=2-4]
\arrow[tail reversed, from=1-4, to=1-5]
\arrow[dotted, no head, from=11-1, to=11-7]
\arrow[dotted, no head, from=10-1, to=10-7]
\arrow[dotted, no head, from=6-1, to=6-7]
\arrow[from=5-4, to=7-4]
\arrow[from=7-4, to=8-4]
\arrow[from=8-4, to=9-4]
\end{tikzcd}\]

% inacc -/> worldly: Skolem
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