Large Veblen ordinal

From Wikipedia, the free encyclopedia
Jump to: navigation, search

In mathematics, the large Veblen ordinal is a certain large countable ordinal, named after Oswald Veblen.

There is no standard notation for ordinals beyond the Feferman–Schütte ordinal Γ0. Most systems of notation use symbols such as ψ(α), θ(α), ψα(β), 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 large Veblen ordinal is sometimes denoted by \phi_{{\Omega^\Omega}}(0) or \theta(\Omega^\Omega) or \psi(\Omega^{\Omega^\Omega}). It was constructed by Veblen using an extension of Veblen functions allowing infinitely many arguments.

References[edit]

  • Veblen, Oswald (1908), "Continuous Increasing Functions of Finite and Transfinite Ordinals", Transactions of the American Mathematical Society 9 (3): 280–292, doi:10.2307/1988605 
  • Weaver, Nik (2005), Predicativity beyond Gamma_0, arXiv:math/0509244