Normal function: Difference between revisions
Jump to navigation
Jump to search
m
no edit summary
(Created page with "A normal function is a function on ordinals that preserves limits and is strictly increasing. That is, \(f\) is normal if and only if it satisfies the following properties: * \(\alpha<\beta \Leftrightarrow f(\alpha)<f(\beta)\) * \(f(\alpha)=\sup f(\beta)\) if and only if \(\beta<\alpha\) and \(\alpha\) is a limit ordinal.") |
CreeperBomb (talk | contribs) mNo edit summary |
||
| (3 intermediate revisions by 2 users not shown) | |||
Line 1:
A normal function is
* \(\alpha<\beta \Leftrightarrow f(\alpha)<f(\beta)\)
* \(f(\alpha)=\sup \{ 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.
| |||