From f9d3012c3a6eff841ab6ab6a74788b31d90b84ec Mon Sep 17 00:00:00 2001
From: "David A. Madore" <david+git@madore.org>
Date: Sat, 29 Jul 2017 21:42:18 +0200
Subject: Add some more references to Simpson's SoSOA.

---
 ordinal-zoo.tex | 10 ++++++++--
 1 file changed, 8 insertions(+), 2 deletions(-)

(limited to 'ordinal-zoo.tex')

diff --git a/ordinal-zoo.tex b/ordinal-zoo.tex
index 54b4f82..86cde74 100644
--- a/ordinal-zoo.tex
+++ b/ordinal-zoo.tex
@@ -189,14 +189,20 @@ subsets of $\omega$, and they are also exactly the subsets recursive
 \ordinal $\omega_\omega^{\mathrm{CK}}$: the smallest limit of
 admissibles.  This ordinal is not admissible.  This is the smallest
 $\alpha$ such that $L_\alpha \cap \mathscr{P}(\omega)$ is a model of
-$\Pi^1_1$-comprehension.
+$\Pi^1_1$-comprehension (cf. \cite[theorem VII.1.8 on p. 246 and
+  theorem VII.5.17 on p. 292 and notes to §VII.5 on
+  p. 293]{Simpson2009}).
 
 \ordinal\label{RecursivelyInaccessible} The smallest recursively
 inaccessible ordinal: this is the smallest ordinal which is admissible
 and limit of admissibles.  This is the smallest ordinal $\alpha$ such
 that $L_\alpha \models \mathsf{KPi}$, or, on the arithmetical side,
 such that $L_\alpha \cap \mathscr{P}(\omega)$ is a model of
-$\Delta^1_2$-comprehension.  (Compare •\ref{CollapseInaccessible}.)
+$\Delta^1_2$-comprehension (cf. \cite[theorem VII.3.24 on p. 267 and
+  theorem VII.5.17 on p. 292 and
+  errata\footnote{\url{http://www.personal.psu.edu/t20/sosoa/typos.pdf}}
+  to notes to §VII.5 on p. 293]{Simpson2009}).
+(Compare •\ref{CollapseInaccessible}.)
 
 This is the smallest ordinal $\omega_1^{\mathsf{E}_1}$ not the order
 type of a well-ordering recursive in the Tugué
-- 
cgit v1.2.3

