Normal function: Difference between revisions

A normal function is an [[ordinal function]] that preserves limits and is strictly increasing. That is, \(f\) is normal if and only if it satisfies the following properties:

* \(\alpha<\beta \Leftrightarrow f(\alpha)<f(\beta)\)

Veblen's fixed point lemma, which is essential for constructing the [[Veblen hierarchy]], guarantees that, not only does every normal function have a [[fixed point]], but the class of fixed points is unbounded and their enumeration function is also normal.