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authorDavid A. Madore <david+git@madore.org>2013-02-07 15:38:47 (GMT)
committerDavid A. Madore <david+git@madore.org>2013-02-07 15:38:47 (GMT)
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Add a note about not including large cardinals.
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@@ -430,6 +430,20 @@ $\Delta^1_2$ (resp. $\Sigma^1_2$) subsets of $\omega$
This is also the smallest $\Sigma^1_2$-reflecting ordinal
(\cite{Richter1975}).
+\bigbreak
+
+\textbf{\textcolor{orange}{Note:}} This document should probably not
+start listing large cardinals, because \textbf{(0)} the fact that one
+implies the other nonwithstanding, this is about “ordinals”, not
+“cardinals”, \textbf{(1)} they are already well covered elsewhere
+(see, e.g., \cite{Kanamori1997}) and \textbf{(2)} we don't want to
+start making assumptions, e.g., about whether $\omega_1^L$ is or is
+not equal to $\omega_1$, but without making such assumptions it is no
+longer possible to correctly order definitions. Perhaps a median way
+would be to assume $V=L$ for ordering, forget about measurable
+cardinals and whatnot, and still include inaccessibles, Mahlo, weakly
+compact, etc.
+
%
%
%
@@ -587,6 +601,10 @@ so $A \in L_\gamma$ with $\gamma$ countable, as asserted.
$R$-operator and the ordinal $\sigma_3$”, \textit{J. Symbolic Logic}
\textbf{51} (1986), 1–11.
+\bibitem[Kanamori1997]{Kanamori1997} Akihiro Kanamori, \textit{The
+ Higher Infinite} (corrected first edition), Perspectives in
+ Mathematical Logic, Springer-Verlag (1997), ISBN 3-540-57071-3.
+
\bibitem[MarekSrebrny1973]{MarekSrebrny1973} Wiktor Marek \& Marian
Srebrny, “Gaps in the Constructible Universe”,
\textit{Ann. Math. Logic} \textbf{6} (1974), 359–394.