List of ordinals: Difference between revisions
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== Countable ordinals ==
In this list we assume there is a transitive model of ZFC. The \(\psi\) is Extended Buchholz unless specified.<!--Necessary to compare ordinals such as "least a such that L_a models ZFC"-->
* [[0]], the smallest ordinal
* [[1]], the first successor ordinal
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* [[omega^3|\( \omega^{3} \)]]
* [[omega^omega|\( \omega^{\omega} \)]]
* [[epsilon_numbers#zero|\( \psi_{0}(\Omega) = \varphi(1,0) = \varepsilon_{0} \)]]<sup>(sort out page)</sup>
* [[veblen_hierarchy#zeta|\( \psi_{0}(\Omega^{2}) = \varphi(2,0) = \zeta_{0} \)]]<sup>(decide if own page)</sup>
* [[veblen_hierarchy|\( \psi_{0}(\Omega^{\omega}) = \varphi(\omega,0) \)]]
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* [[buchholz_ordinal|\( \psi_{0}(\Omega_{\omega}) \)]], the BO (Buchholz ordinal)
* [[takeuti-feferman-buchholz_ordinal|\( \psi_{0}(\varepsilon_{\Omega_{\omega} + 1}) \)]], the TFBO (Takeuti-Feferman-Buchholz ordinal)
* [[Bird's ordinal|\( \psi_{0}(\Omega_\Omega) \)]], sometimes known as Bird's ordinal
* [[extened_buchholz_ordinal|\( \psi_{0}(\Omega_{\Omega_{\dots}}) \)]], the EBO (Extended Buchholz ordinal)
* \( \psi_{\Omega}(\varepsilon_{\chi_1(0)+1}) \), the PTO of KPi (in Rathjen's Mahlo OCF, also applies to the one below)
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