The Veblen Hierarchy
In the special case when φ0(α)=ωα this family of functions is known as the Veblen hierarchy. The function φ1 is the same as the ε function: φ1(α)= εα. If then From this and the fact that φβ is strictly increasing we get the ordering: if and only if either ( and ) or ( and ) or ( and ).
Read more about this topic: Veblen Function
Famous quotes containing the word hierarchy:
“In a hierarchy every employee tends to rise to his level of incompetence.”
—Laurence J. Peter (1919–1990)