List of ordinals: Difference between revisions
Jump to navigation
Jump to search
Content added Content deleted
Augigogigi (talk | contribs) No edit summary |
No edit summary |
||
Line 1: | Line 1: | ||
== Countable ordinals == |
== Countable ordinals == |
||
In this list we assume there is a transitive model of ZFC.<!--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.<!--Necessary to compare ordinals such as "least a such that L_a models ZFC"--> |
||
* [[0]], the smallest ordinal |
* [[0]], the smallest ordinal |
||
* [[1]], the first successor ordinal |
* [[1]], the first successor ordinal |
||
Line 18: | Line 18: | ||
* [[takeuti-feferman-buchholz_ordinal|\( \psi_{0}(\varepsilon_{\Omega_{\omega} + 1}) \)]], the TFB (Takeuti-Feferman-Buchholz ordinal) |
* [[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) |
* [[extened_buchholz_ordinal|\( \psi_{0}(\Omega_{\Omega_{\dots}}) \)]], the EBO (Extended Buchholz ordinal) |
||
* \( \psi_{\Omega}(\varepsilon_{ |
* \( \psi_{\Omega}(\varepsilon_{\chi_1(0)+1}) \), the PTO of KPi (in Rathjen's Mahlo OCF, also applies to the one below) |
||
* \( \psi_{\Omega}(\psi_{\chi_{\varepsilon_{M+1}}(0)}(0)) \), the PTO of KPM |
* \( \psi_{\Omega}(\psi_{\chi_{\varepsilon_{M+1}}(0)}(0)) \), the PTO of KPM |
||
* \( \Psi^{0}_{\Omega}(\varepsilon_{K+1}) \), the PTO of KP+\(\Pi_{3}\)-refl. |
* \( \Psi^{0}_{\Omega}(\varepsilon_{K+1}) \), 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 |
* \( \psi_\Omega(\varepsilon_{\mathbb{K}+1}) \), 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 |
* \( \Psi_{\mathbb{X}}^{\varepsilon_{\Upsilon+1}} \), the limit of Jan-Carl Stegert's second [[ordinal_collapsing_function|OCF]] using indescribable cardinals |