Veblen function

The Veblen function is used to obtain larger ordinal numbersMathworldPlanetmath than those provided by exponentiationMathworldPlanetmathPlanetmath. It builds on a hierarchy of closed and unboundedPlanetmathPlanetmath classes:

  • Cr(0) is the additively indecomposable numbers,

  • Cr(Sn)=Cr(n) the set of fixed points of the enumerating function of Cr(n)

  • Cr(λ)=α<λCr(α)

The Veblen function φαβ is defined by setting φα equal to the enumerating function of Cr(α).

We call a number α strongly critical if αCr(α). The class of strongly critical ordinals is written 𝐒𝐂, and the enumerating function is written f𝐒𝐂(α)=Γα.

Γ0, the first strongly critical ordinal, is also called the Feferman-Schutte ordinal.

Title Veblen function
Canonical name VeblenFunction
Date of creation 2013-03-22 13:29:10
Last modified on 2013-03-22 13:29:10
Owner Henry (455)
Last modified by Henry (455)
Numerical id 4
Author Henry (455)
Entry type Definition
Classification msc 03E10
Classification msc 03F15
Defines strongly critical
Defines Feferman-Schutte ordinal