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| -rw-r--r-- | ordinal-zoo.tex | 16 |
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 |