Improve some references.

1 files changed, 9 insertions, 4 deletions

diff --git a/ordinal-zoo.tex b/ordinal-zoo.tex
index 81c37ca..54b4f82 100644
--- a/ordinal-zoo.tex
+++ b/ordinal-zoo.tex
@@ -182,7 +182,9 @@ subsets of $\omega$, and they are also exactly the subsets recursive
 [this is stated vaguely and without proof in \cite[§2, introductory
     remarks]{HinmanMoschovakis1971}, and also alluded to, but with an
   argument, in \cite[chapter VI, introductory remarks to §6 on
-    p. 316]{Hinman1978}]).
+    p. 316]{Hinman1978}; but the essential argument should be Gandy's
+  selection theorem, \cite[chapter VI, theorem 4.1 on
+    p. 292 or its corollary 4.3 on p. 294]{Hinman1978}]).
 
 \ordinal $\omega_\omega^{\mathrm{CK}}$: the smallest limit of
 admissibles.  This ordinal is not admissible.  This is the smallest
@@ -212,7 +214,8 @@ equivalently, the smallest admissible $\alpha$ such that any ordering
 which $L_\alpha$ thinks is a well-ordering is, indeed, a
 well-ordering: see \cite[theorem 6.1 on p. 291]{Nadel1973}
 (compare \cite{Harrison1968} for the negative result concerning the
-ordinal $\omega_1^{\mathrm{CK}}$ of •\ref{ChurchKleene}).
+ordinal $\omega_1^{\mathrm{CK}}$ of •\ref{ChurchKleene}; compare also
+\cite{Gostanian1979} and •\ref{SigmaOneOne} for related facts).
 
 \ordinal The smallest recursively hyperinaccessible ordinal: i.e., the
 smallest recursively inaccessible which is a limit of recursively
@@ -304,8 +307,10 @@ 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}, \cite[\FINDTHIS:
-  where ?]{AbramsonSacks1976} and \cite[theorem 3.3]{Gostanian1979}.
+\cite[theorem 6.6 on p. 377]{Simpson1978} and
+\cite[theorem 3.3]{Gostanian1979} (on the terminology ``Gandy
+ordinal'', see \cite{AbramsonSacks1976}: in \cite{Gostanian1979} the
+same ordinals are called ``good'').
 
 [\FINDTHIS: how stable is this ordinal?]