From 18276c8a7f480670b9582dbd1a6387725df1421b Mon Sep 17 00:00:00 2001
From: "David A. Madore" <david+git@madore.org>
Date: Tue, 17 Nov 2015 15:54:05 +0100
Subject: Add references to papers by Gostanian.

---
 ordinal-zoo.tex | 16 ++++++++++++----
 1 file changed, 12 insertions(+), 4 deletions(-)

(limited to 'ordinal-zoo.tex')

diff --git a/ordinal-zoo.tex b/ordinal-zoo.tex
index b7a64cd..81c37ca 100644
--- a/ordinal-zoo.tex
+++ b/ordinal-zoo.tex
@@ -287,9 +287,9 @@ $\Sigma^1_1$-inductively definable subsets of $\omega$
 (\cite[theorem D on p. 304]{RichterAczel1974}; see
 also \cite[example 4.14 on p. 370]{Simpson1978}).
 
-That this ordinal is gerater than that of •\ref{PiOneOne}:
+That this ordinal is greater than that of •\ref{PiOneOne}:
 \cite[corollary 1 to theorem 6 on p.213]{Aanderaa1974}; also see:
-\cite[theorem 6.5]{Simpson1978}.
+\cite[theorem 6.5]{Simpson1978} and \cite{GostanianHrbacek1979}.
 
 This is the smallest ordinal $\omega_1^{\mathsf{E}_1^\#}$ not the
 order type of a well-ordering recursive in the nondeterministic
@@ -304,8 +304,8 @@ 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}.
+\cite[theorem 6.6 on p. 377]{Simpson1978}, \cite[\FINDTHIS:
+  where ?]{AbramsonSacks1976} and \cite[theorem 3.3]{Gostanian1979}.
 
 [\FINDTHIS: how stable is this ordinal?]
 
@@ -599,6 +599,14 @@ so $A \in L_\gamma$ with $\gamma$ countable, as asserted.
   \textit{Constructibility}, Perspectives in Mathematical
   Logic \textbf{6}, Springer-Verlag (1984), ISBN 3-540-13258-9.
 
+\bibitem[Gostanian1979]{Gostanian1979} Richard Gostanian “The next
+  admissible ordinal”, \textit{Ann. Math. Logic} \textbf{17} (1979),
+  171–203.
+
+\bibitem[GostanianHrbáček1979]{GostanianHrbacek1979} Richard Gostanian
+  \& Karel Hrbáček, “A new proof that $\pi^1_1 < \sigma^1_1$”,
+  \textit{Z. Math. Logik Grundlag. Math.} \textbf{25} (1979), 407–408.
+
 \bibitem[Harrington1974]{Harrington1974} Leo Harrington, “The
   Superjump and the first Recursively Mahlo Ordinal”, \textit{in}:
   Jens Erik Fenstad \& Peter G. Hinman (eds.), \textit{Generalized
-- 
cgit v1.2.3

