From 72ac39542e5c463de5751c1392cf17220334c02b Mon Sep 17 00:00:00 2001
From: "David A. Madore" <david+git@madore.org>
Date: Thu, 7 Feb 2013 17:40:40 +0100
Subject: Note on Gandy ordinals.

---
 ordinal-zoo.tex | 11 +++++++++++
 1 file changed, 11 insertions(+)

(limited to 'ordinal-zoo.tex')

diff --git a/ordinal-zoo.tex b/ordinal-zoo.tex
index 540f8ef..54cdc13 100644
--- a/ordinal-zoo.tex
+++ b/ordinal-zoo.tex
@@ -289,6 +289,13 @@ subsets recursive (resp. semi-recursive) in $\mathsf{E}_1^\#$ (combine
 \cite[theorem 1 on p. 313, theorem 2 on p. 318]{Aczel1970} and
 \cite[theorem D on p. 304]{RichterAczel1974}).
 
+This is the smallest admissible $\alpha$ which is not Gandy, i.e.,
+such that every $\alpha$-recursive linear ordering of $\alpha$ of
+which $L_{\alpha^+}$ thinks that it is a well-ordering (with
+$\alpha^+$ being the next admissible) is, indeed, a well-ordering: see
+\cite[theorem 6.6 on p. 377]{Simpson1978} and \cite[\FINDTHIS:
+  where ?]{AbramsonSacks1976}.
+
 [\FINDTHIS: how stable is this ordinal?]
 
 \ordinal The smallest $(^{++})$-stable ordinal, i.e., the smallest
@@ -540,6 +547,10 @@ so $A \in L_\gamma$ with $\gamma$ countable, as asserted.
 
 \begin{thebibliography}{}
 
+\bibitem[AbramsonSacks1976]{AbramsonSacks1976} Fred G. Abramson \&
+  Gerald E. Sacks, “Uncountable Gandy Ordinals”, \textit{J. London
+    Math. Soc. (2)} \textbf{14} (1976), 387–392.
+
 \bibitem[Aczel1970]{Aczel1970} Peter Aczel, “Representability in Some
   Systems of Second Order Arithmetic”, \textit{Israel J. Math}
   \textbf{8} (1970), 308–328.
-- 
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