Ordinal function: Difference between revisions
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An '''ordinal function''' refers to a function from [[ordinal]]s to ordinals. More rarely, they refer to functions from an initial segment of the ordinals to another. Important examples include [[continuous function]]s and [[normal function]]s.
Technically speaking and within [[ZF]], since [[Burali–Forti paradox|ordinals don't form a set]], one can't formally talk about functions \(f:\text{On}\to\text{On}\). However, as with the method of using Grothendieck universes, replacing \(\text{On}\) with the set of ordinals below a large enough ordinal, such as an [[inaccessible ordinal]] or even an [[uncountable]]<ref>D. Probst,
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