**admissible**if \(L_\alpha\) is an admissible set, where \(L\) is Gödel's constructible universe.^{[1]}For successor ordinal \(\alpha\), \(1+\alpha\)-th admissible ordinal is denoted by \(\omega_\alpha^\text{CK}\). For example, \(\omega_\omega^\text{CK}\) is not admissible but it is a limit of admissibles. An ordinal is called to be

## Sources

## See also

**Basics:** cardinal numbers · normal function · ordinal notation · ordinal numbers · fundamental sequence · ordinal collapsing function**Theories:** Presburger arithmetic · Peano arithmetic · KP · second-order arithmetic · ZFC**Countable ordinals:** \(\omega\) · \(\varepsilon_0\) · \(\zeta_0\) · \(\Gamma_0\) · \(\vartheta(\Omega^3)\) · \(\vartheta(\Omega^\omega)\) · \(\vartheta(\Omega^\Omega)\) · \(\vartheta(\varepsilon_{\Omega + 1}) = \psi(\Omega_2)\) · \(\psi(\Omega_\omega)\) · \(\psi(\varepsilon_{\Omega_\omega + 1})\) · \(\psi(\psi_I(0))\) · \(\omega_1^\mathfrak{Ch}\) · \(\omega_1^\text{CK}\) · **\(\omega_\alpha^\text{CK}\)** · \(\lambda,\zeta,\Sigma,\gamma\) · List of countable ordinals**Ordinal hierarchies:** Fast-growing hierarchy · Slow-growing hierarchy · Hardy hierarchy · Middle-growing hierarchy · N-growing hierarchy**Uncountable cardinals:** \(\omega_1\) · omega fixed point · inaccessible cardinal \(I\) · Mahlo cardinal \(M\) · weakly compact cardinal \(K\) · indescribable cardinal · rank-into-rank cardinal · more...