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Line 59: * The least admissible \(\alpha\) so that \(L_\alpha\) satisfies arithmetically quasi-induction = the least admissible \(\alpha\) so that, for all \(x \in \mathcal{P}(\omega) \cap L_\alpha\), there are \(\xi, \sigma < \alpha\) so that \(L_\xi[x] \prec_{\Sigma_2} L_\sigma[x]\)<ref name="Welch2010Draft" /> * Least \(\beta\) where \(L_\beta\) starts a chain of \(\Sigma_3\)-elementary substructures <ref name="Welch2010Draft" /> * The smallest [[~~gap_ordinals\|~~gap ordinal]]<ref name="Gaps">W. Marek, M. Srebrny, [https://www.sciencedirect.com/science/article/pii/0003484374900059 Gaps in the Constructible Universe] (1973). Accessed 7 September 2022.</ref> = the least simultaneously \(\Sigma_n\)-nonprojectible ordinal for all \(n\)<ref>The Higher Infinite in Proof Theory, Michael Rathjen</ref> <!-- I'd like to put "least a so that some ordinal is undefinable in L_a", which is the same as the "least a so that L_b < L_a for some b < a", which is obviously bigger than the least gap ordinal. I don't know exactly where it lies, though. --> Least start of a gap in the constructible universe of length 2<ref name="Gaps" />

List of ordinals: Difference between revisions

List of ordinals (edit)