In mathematics, the large Veblen ordinal is a certain

large countable ordinal In the mathematical discipline of set theory, there are many ways of describing specific countable ordinals. The smallest ones can be usefully and non-circularly expressed in terms of their Cantor normal forms. Beyond that, many ordinals of rele ...

, named after

Oswald Veblen Oswald Veblen (June 24, 1880 – August 10, 1960) was an American mathematician, geometer and topologist, whose work found application in atomic physics and the theory of relativity. He proved the Jordan curve theorem in 1905; while this was lon ...

. There is no standard notation for ordinals beyond the

Feferman–Schütte ordinal In mathematics, the Feferman–Schütte ordinal Γ0 is a large countable ordinal. It is the proof-theoretic ordinal of several mathematical theories, such as arithmetical transfinite recursion. It is named after Solomon Feferman and Kurt Schütte, ...

Γ₀. Most systems of notation use symbols such as ψ(α), θ(α), ψ_α(β), some of which are modifications of the

Veblen function In mathematics, the Veblen functions are a hierarchy of normal functions ( continuous strictly increasing functions from ordinals to ordinals), introduced by Oswald Veblen in . If φ0 is any normal function, then for any non-zero ordinal α, φ ...

s to produce countable ordinals even for uncountable arguments, and some of which are ordinal collapsing functions. The large Veblen ordinal is sometimes denoted by

\phi_(0)

\theta(\Omega^\Omega)

\psi(\Omega^)

. It was constructed by Veblen using an extension of Veblen functions allowing infinitely many arguments.

References

* * {{Number-stub Ordinal numbers