diff options
| -rw-r--r-- | ordinal-zoo.tex | 10 |
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 |