Large Veblen ordinal

The large Veblen ordinal is a large countable ordinal. In the Veblen hierarchy as extended to transfinitely many arguments (also called Schutte's Klammersymbolen), it is the least fixed point of the ordinal function \(\alpha \mapsto \varphi \left( \begin{array}{c} 1 \\ \alpha \end{array} \right)\). Using Weiermann's \(\vartheta\) function, it can also be denoted \(\vartheta(\Omega^\Omega)\) and is the first fixed point of \(\alpha \mapsto \vartheta(\Omega^\alpha)\). Additionally, using Madore's \(\psi\) function or Buchholz's \(\psi\) function, it is equal to \(\psi_0(\Omega^{\Omega^\Omega})\). This ordinal has also been called the "Great Veblen number" and denoted as \(E(0)\).

Jonathan Bowers has mentioned "LVO-order set theory" while discussing hypothetical ways to beat Rayo's number without defining it.