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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]] Γ<sub>0</sub>. Most systems of notation use symbols such as ψ(α), θ(α), ψ<sub>α</sub>(β), some of which are modifications of the [[Veblen function]]s to produce countable ordinals even for uncountable arguments, and some of which are "collapsing functions".
 
The '''large Veblen ordinal''' is sometimes denoted by <math>\phi_{{\Omega^\Omega}}(0)</math> or <math>\theta(\Omega^\Omega)</math> or <math>\psi(\Omega^{\Omega^\Omega})</math>. It was constructed by Veblen using an extension of Veblen functions allowing infinitely many arguments.
 
==References==
*{{citation|title= Continuous Increasing Functions of Finite and Transfinite Ordinals |first= Oswald |last=Veblen |journal= Transactions of the American Mathematical Society|volume= 9|issue= 3|year= 1908|pages=280–292 |doi= 10.2307/1988605}}
*{{citation|last=Weaver|first=Nik|arxiv=math/0509244|title=Predicativity beyond Gamma_0|year=2005}}
{{countable ordinals}}
 
[[Category:Ordinal numbers]]

Revision as of 00:48, 29 January 2014

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 ϕΩΩ(0) or θ(ΩΩ) or ψ(ΩΩΩ). It was constructed by Veblen using an extension of Veblen functions allowing infinitely many arguments.

References

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