List of countable ordinals

Smaller numbers
 * Omega (\(\omega\))
 * Epsilon (\(\varepsilon_0\))
 * Cantor (\(\zeta_0\))
 * Feferman-Schutte Ordinal (\(\Gamma_0\))
 * Ackermann Ordinal (\(\varphi(1,0,0,0)\))
 * Small Veblen Ordinal (\(\vartheta(\Omega^\omega)\))
 * Large Veblen Ordinal (\(\vartheta(\Omega^\Omega)\))
 * Bachmann-Howard Ordinal (\(\psi(\varepsilon_{\Omega+1})\))
 * First Psi Ordinal (\(\psi(\Omega_\omega)\))
 * Takeuti-Feferman-Buchholz Ordinal (\(\psi(\varepsilon_{\Omega_\omega+1})\))
 * Third Psi Ordinal (\(\psi(\psi_I(0))\))
 * Omega One Chess
 * Church-Kleene Ordinal
 * Infinite Time Turing Machine Ordinals