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 \(E(0)\)M. Rathjen, The art of ordinals analysis (p.55, 2006, accessed 2020-11-11).
Jonathan Bowers has mentioned "LVO-order set theory" while discussing hypothetical ways to beat Rayo's number without defining it.Bowers, Jonathan. Going to Oblivion. Retrieved 2016-12-14.
In the fast-growing hierarchy, using Bird's array notation \(f_{\vartheta(\Omega^{\Omega})}(n)\) is approximately {n,n [1 [1 ¬ 1 ¬ 2] 2] 2} in the Nested Hyper-Nested Array Notation,Bird, Chris. Beyond Bird’s Nested Arrays II. and {n,n [1 [1 / 1 / 2 ~ 2] 2] 2} in the Hierarchial Hyper-Nested Array Notation.Bird, Chris. Beyond Bird’s Nested Arrays IV.
== Sources ==
== See also ==
zh:大凡勃倫序
ja:大ヴェブレン順序数
Category:Transfinite ordinals
ru:Большой ординал Веблена