List of ordinals: Difference between revisions
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* [[veblen_hierarchy#zeta|\( \psi_{0}(\Omega^{2}) = \varphi(2,0) = \zeta_{0} \)]]<sup>(decide if own page)</sup>
* [[veblen_hierarchy|\( \psi_{0}(\Omega^{\omega}) = \varphi(\omega,0) \)]], the second infinite primitive recursively principal ordinal
* [[feferman-schutte_ordinal|\( \psi_{0}(\Omega^{\Omega}) = \varphi(1,0,0) = \Gamma_{0} \)]], the Feferman-Schutte ordinal and the PTO of ATR<sub>0</sub>. This is the least \(\alpha\) such that \(L_\alpha\cap\mathcal P(\omega)\) satisfies Feferman's theory \(\mathrm{IR}\).<ref>S. G. Simpson, "[https://sgslogic.net/t20/talks/feferfest/paper3.pdf Predicativity: The Outer Limits]" (2000), p.3. Accessed 30 January 2024.</ref>
* [[the_veblen_hierarchy#ackermann|\( \psi_{0}(\Omega^{\Omega^{2}}) = \varphi(1,0,0,0) \)]], the Ackermann Ordinal<sup>(decide if keep)</sup>
* [[small_veblen_ordinal|\( \psi_{0}(\Omega^{\Omega^{\omega}}) = \varphi\begin{pmatrix}1 \\ \omega\end{pmatrix} \)]], the SVO (Small Veblen ordinal)
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** \( \zeta \), the supremum of all eventually writable ordinals = the least \( \Sigma_2 \)-extendible ordinal
** \( \Sigma \), the supremum of all accidentally writable ordinals = the least target of \( \Sigma_2 \)-stability
* The least ordinal in \(
* The least ordinal in \(E_\eta\), for \(\eta > 1\)<ref name="Welch2010Draft" />
* The least admissible \(\alpha\) so that \(L_\alpha\) satisfies
* Least \(\beta\) where \(L_\beta\) starts a chain of \(\Sigma_3\)-elementary substructures <ref name="Welch2010Draft" />
* The smallest [[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 \(n<\omega\)<ref>The Higher Infinite in Proof Theory, Michael Rathjen</ref>
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