Circulation and the Fast-Growing Hierarchy

Circulation and the Fast-Growing Hierarchy - Printable Version

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RE: Circulation and the Fast-Growing Hierarchy - Catullus - 09/24/2022

(06/07/2022, 01:48 AM)Catullus Wrote: I wonder how omega minus one would behave in some sort of extension of the Fast-growing hierarchy. I know omega minus one is not an ordinal. But it is a Hyperreal number.
$[Image: svg.image?f_%7B\omega-1%7D(x)]$ would a be a sequence, such that when applied x time to x it results in $[Image: svg.image?f_\omega(x)]$ . What about extending the Fast-growing hierarchy to other Hyperreals? such as omega minus 2?

Extending the Fast-growing hierarchy to things like $[Image: svg.image?f_%7B\omega-1%7D(x)]$ has already been discussed here.