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authorDavid A. Madore <david+git@madore.org>2015-11-12 03:10:02 (GMT)
committerDavid A. Madore <david+git@madore.org>2015-11-12 03:10:02 (GMT)
commitd57d142e4786f8998256994bcdc375450b3cccea (patch)
tree99c98c301ce856ebcff69f245254d788a2c4aa42
parenta5ee587a783006ce70dc570540d708877f23323d (diff)
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Add a pseudo-reference for a statement that needs to be checked.
-rw-r--r--ordinal-zoo.tex10
1 files changed, 8 insertions, 2 deletions
diff --git a/ordinal-zoo.tex b/ordinal-zoo.tex
index 14cd108..bc06fcb 100644
--- a/ordinal-zoo.tex
+++ b/ordinal-zoo.tex
@@ -178,8 +178,9 @@ The $\omega_1^{\mathrm{CK}}$-recursive
(resp. $\omega_1^{\mathrm{CK}}$-semi-recursive) subsets of $\omega$
are exactly the $\Delta^1_1$ (=hyperarithmetic) (resp. $\Pi^1_1$)
subsets of $\omega$, and they are also exactly the subsets recursive
-(resp. semi-recursive) in $\mathsf{E}$ (or $\mathsf{E}^\#$,
-\CHECKTHIS).
+(resp. semi-recursive) in $\mathsf{E}$ (or $\mathsf{E}^\#$, \CHECKTHIS
+[this is stated vaguely and without proof in \cite[§2, introductory
+ remarks]{HinmanMoschovakis1971}]).
\ordinal $\omega_\omega^{\mathrm{CK}}$: the smallest limit of
admissibles. This ordinal is not admissible. This is the smallest
@@ -615,6 +616,11 @@ so $A \in L_\gamma$ with $\gamma$ countable, as asserted.
Mathematical Logic \textbf{9}, Springer-Verlag (1978),
ISBN 3-540-07904-1.
+\bibitem[HinmanMoschovakis1971]{HinmanMoschovakis1971} Peter G. Hinman
+ \& Yiannis N. Moschovakis, “Computability over the Continuum”,
+ \textit{in}: R. O. Gandy \& C. M. E. Yates (eds.), \textit{Logic
+ Colloquium '69} (Manchester, 1969), North-Holland (1971), 77–105.
+
\bibitem[JaegerPohlers1983]{JaegerPohlers1983} Gerhard Jäger \&
Wolfram Pohlers, “Eine beweistheoretische Untersuchung von
($\Delta^1_2$-$\mathsf{CA}$)+($\mathsf{BI}$) und verwandter