[FOM] Transfinite Recursion in Functional Analysis and Measure Theory
Kenny Easwaran
easwaran at gmail.com
Tue Jan 29 10:49:40 EST 2019
I'm not sure that this is quite measure theory, but I believe that
Cantor invented his concepts of the transfinite in order to prove the
Cantor-Bendixson theorem. If you iterate the process of removing
isolated points from a set, you must terminate in some countable
number of steps, and each step involves removing at most countably
many points. The remaining set is either perfect or empty. He noticed
that in general, you need to iterate more than just finitely many
times or omega many times, but can only need to iterate a countable
number of times, and developed the theory of ordinals to do this.
https://en.wikipedia.org/wiki/Derived_set_(mathematics)
Kenny Easwaran
On Tue, Jan 29, 2019 at 12:07 AM Adam Kolany <dr.a.kolany at wp.pl> wrote:
>
> Hi,
>
> I would appreciate examples of proofs in FA and MT where Transfinite
> Recursion was used.
>
> Also "sensible" formulations of TR in ZF set theory would be welcome.
>
>
> Can you help ?
>
>
> regards,
>
> Adam Kolany
>
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