diff options
authorDavid A. Madore <>2015-11-17 15:54:05 +0100
committerDavid A. Madore <>2015-11-17 15:54:05 +0100
commit18276c8a7f480670b9582dbd1a6387725df1421b (patch)
parent4e11b97de71e1fe3c49cc86132a8fa33bea3d872 (diff)
Add references to papers by Gostanian.
1 files changed, 12 insertions, 4 deletions
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