The large Veblen ordinal is a large countable ordinal. In the Veblen hierarchy as extended to transfinitely many arguments, it is the first fixed point of \(\alpha \mapsto \varphi_{\Omega^\alpha}(0)\). Using Weiermann's \(\vartheta\) function, it can also be denoted \(\vartheta(\Omega^\Omega)\) and is the first fixed point of \(\alpha \mapsto \theta(\Omega^\alpha)\). Additionally, using Madore's psi function, it is equal to \(\psi(\Omega^{\Omega^\Omega})\).

Jonathan Bowers mentioned "LVO-order set theory" while discussing hypothetical ways to beat Rayo's number.[1]


  1. Bowers, Jonathan. Going to Oblivion. Retrieved 2016-12-14.

See also

Ordinals, ordinal analysis and set theory

Basics: cardinal numbers · normal function · ordinal notation · ordinal numbers · fundamental sequence
Theories: Presburger arithmetic · Peano arithmetic · KP · second-order arithmetic · ZFC
Countable ordinals: \(\omega\) · \(\varepsilon_0\) · \(\zeta_0\) · \(\Gamma_0\) · \(\vartheta(\Omega^3)\) · \(\vartheta(\Omega^\omega)\) · \(\vartheta(\Omega^\Omega)\) · \(\vartheta(\varepsilon_{\Omega + 1})\) · \(\psi(\Omega_\omega)\) · \(\psi(\varepsilon_{\Omega_\omega + 1})\) · \(\psi(\psi_I(0))\)‎ · \(\omega_1^\mathfrak{Ch}\) · \(\omega_1^\text{CK}\) · \(\lambda,\zeta,\Sigma,\gamma\) · 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...

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