Ordinal numbers

Small Veblen ordinal

In mathematics, the small Veblen ordinal is a certain large countable ordinal, named after Oswald Veblen. It is occasionally called the Ackermann ordinal, though the Ackermann ordinal described by is somewhat smaller than the small Veblen ordinal. There is no standard notation for ordinals beyond the Feferman–SchΓΌtte ordinal . Most systems of notation use symbols such as , , , some of which are modifications of the Veblen functions to produce countable ordinals even for uncountable arguments, and some of which are "collapsing functions". The small Veblen ordinal or is the limit of ordinals that can be described using a version of Veblen functions with finitely many arguments. It is the ordinal that measures the strength of Kruskal's theorem. It is also the ordinal type of a certain ordering of rooted trees. (Wikipedia).

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Related pages

Feferman–SchΓΌtte ordinal | Large countable ordinal | Ackermann ordinal | Veblen function | Oswald Veblen