List of ordinals: Difference between revisions
no edit summary
No edit summary |
No edit summary |
||
Line 59:
* The least (next \( \Pi_n \)-reflecting ordinal)-stable ordinal, for \( 2<n<\omega \)
* The least doubly \( (+1) \)-stable ordinal<ref name=":0" /><sup>(p.4)</sup>
* The least \(\omega\)-ply stable ordinal = the least ordinal stable up to a nonprojectible ordinal = \(\Sigma^1_2\)-soundness ordinal of \(\Pi^1_2\mathrm{-CA}_0\)<ref name="Pi12Consequences" /><sup>p.24</sup>
* The least nonprojectible ordinal<ref name=":0" /><sup>(p.5)</sup> = the least ordinal \( \Pi_2 \)-reflecting on the ordinals stable up to it = the least limit of \(\omega\)-ply stable ordinals<ref name=":2">E. Kranakis, [https://www.sciencedirect.com/science/article/pii/0003484382900225<nowiki> Reflection and Partition Properties of Admissible Ordinals] (1980). Accessed 7 September 2022.</nowiki></ref><sup>(p.218)</sup>
* The least \( \Sigma_2 \)-admissible ordinal<ref name=":0" /><sup>(pp.5-6)</sup> = least ordinal \( \Pi_3 \)-reflecting on the ordinals stable up to it<ref name=":2" /><sup>(p.221)</sup>
| |||