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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.<!--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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* [[takeuti-feferman-buchholz_ordinal|\( \psi_{0}(\varepsilon_{\Omega_{\omega} + 1}) \)]], the TFB (Takeuti-Feferman-Buchholz ordinal)
* [[extened_buchholz_ordinal|\( \psi_{0}(\Omega_{\Omega_{\dots}}) \)]], the EBO (Extended Buchholz ordinal)
* \( \psi_{\Omega}(\varepsilon_{
* \( \psi_{\Omega}(\psi_{\chi_{\varepsilon_{M+1}}(0)}(0)) \), the PTO of KPM
* \( \Psi^{0}_{\Omega}(\varepsilon_{K+1}) \), the PTO of KP+\(\Pi_{3}\)-refl. (in Rathjen's weakly compact OCF)
* \( \psi_\Omega(\varepsilon_{\mathbb{K}+1}) \), the PTO of KP with a \( \Pi_{\mathbb{N}}\)-refl. universe under ZF + V = L
* \( \Psi_{\mathbb{X}}^{\varepsilon_{\Upsilon+1}} \), the limit of Jan-Carl Stegert's second [[ordinal_collapsing_function|OCF]] using indescribable cardinals
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