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