Large Veblen ordinal

The large Veblen ordinal is a large extension of the small Veblen ordinal. By using an entry-indexing notation (formally defined via finitely-supported ordinal functions), it is possible to further extend the multi-variable version of the Veblen hierarchy used to define the small Veblen ordinal to an array-like system with infinitely long arrays. In particular, the small Veblen ordinal can be denoted by \( \varphi(1,...,0,0) \), with \( \omega \) many zeroes. The new limit of this system is the large Veblen ordinal, or the fixed point of \( \alpha \mapsto \varphi(1 @ \alpha) \), where \( 1 @ \alpha \) denotes a one followed by \( \alpha \) many zeroes. This is another milestone of the recursive ordinals, and may be represented in ordinal collapsing functions as the collapse of \( \Omega^{\Omega^\Omega} \).