Veblen Function - The Veblen Hierarchy

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 ).

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