User blog comment:Ubersketch/Well order to FS/@comment-35470197-20191011140617

> Defining the FS this way most likely makes it uncomputable, but from what I can tell, it works fairly well with calculating FS

No. It is just ill-defined because \(\textrm{lv}(\omega^{\omega}) = \omega^{\omega}\). Namely, the definition of \(\omega^{\omega}[n]\) refers to itself.

> and an algorithm could be made based on this that doesn't necessarily terminate

No. It does not admit an algorithm, because you are considering infinity, which is not encoded into a finite number. Please study the definition of the computability.

> However, there is weirdness such as \(\omega^{\omega}[0]=0\) which I don't know how to fix.

No. It is just ill-defined.