List of ordinals: Difference between revisions
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* <nowiki>\( \Psi_{\mathbb{X}}^{\varepsilon_{\Upsilon+1}} \) where \( \mathbb{X} = (\omega^+; \textsf{P}_0; \epsilon; \epsilon; 0) \), the limit of Jan-Carl Stegert's second </nowiki>[[ordinal_collapsing_function|OCF]] using indescribable cardinals
* PTO of \( \Pi^1_2 \)-comprehension
* PTO of \( \text{Z}_{2} \) = PTO of \(\mathrm{ZFC}\) minus powerset
* PTO of \( \text{KP} + "\omega_1 \) exists \( " \)
* PTO of \( \text{ZFC} \)
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* <nowiki>\( \omega^{\text{CK}}_{\omega} \), the least limit of admissible ordinals = the least height of a model of \( \Pi^1_1 \)-comprehension</nowiki>
* The least recursively inaccessible ordinal = the least height of a model of \( \textsf{KPi} \) or \( \Delta^1_2 \)-comprehension<ref name=":0">D. Madore, [http://www.madore.org/~david/math/ordinal-zoo.pdf A Zoo of Ordinals] (2017). Accessed 7 September 2022.</ref><sup>(p.3)</sup>
* The least recursively Mahlo
* The least recursively hyper-Mahlo ordinal<ref name=":1">W. Richter, P. Aczel, [https://www.duo.uio.no/handle/10852/44063<nowiki> Inductive Definitions and Reflecting Properties of Admissible Ordinals] (1973, preprint, Universitetet i Oslo). Accessed 7 September 2022.</nowiki></ref><sup>(p.13)</sup>
* The least \( \Pi_n \)-reflecting ordinals, for \( 2<n<\omega \)<ref name=":1" />
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* The \( (\sigma^1_1)^n \)-reflecting ordinals for \( 1<n<\omega \)<!--iterated \( \Sigma^1_1 \)-reflection--><ref name="OrderOfReflection" /><sup>(p.20)</sup>
* The least \( (^++1) \)-stable ordinal<sup>(Is this strictly greater than previous entry?)</sup><ref name="OrderOfReflection" /><sup>(p.20)</sup>
* The least (next recursively inaccessible ordinal)-stable ordinal
* The least (next recursively Mahlo ordinal)-stable ordinal
* The least (next \( \Pi_n \)-reflecting ordinal)-stable ordnal, 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
* 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>
* HIGHER STABILITY STUFF GOES HERE<sup>(sort out)</sup>
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* 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>
*<!-- 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" />
* Least \( \beta \) that starts a gap of length \( \beta \)<ref name="Gaps" />
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* [[omega_1|\( \Omega \)]], the smallest [[uncountable]] ordinal
* \( I \), the smallest [[inaccessible_cardinal|inaccessible cardinal]]
* \( M \), the smallest [[
* \( K \), the smallest [[weakly_compact_cardinal|weakly compact cardinal]]
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