List of countable ordinals

Smaller numbers
 * Omega, \(\omega\)
 * Epsilon-zero, \(\varepsilon_0\)
 * Cantor's ordinal, \(\zeta_0\)
 * Feferman–Schütte 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, \(\psi(\varepsilon_{\Omega+1})\)
 * Takeuti-Feferman-Buchholz ordinal, \(\psi(\varepsilon_{\Omega_\omega+1})\)
 * Omega one chess
 * Church-Kleene ordinal
 * Infinite time Turing machine ordinals
 * Church-Kleene ordinal
 * Infinite time Turing machine ordinals