User blog:Ubersketch/Well order to FS

Defining the FS this way most likely makes it uncomputable, but from what I can tell, it works fairly well with calculating FS, and an algorithm could be made based on this by assigning each ordinal a natural number and starting from 0 and climbing up, though this algorithm doesn't necessarily halt. However, there is weirdness such as \(\omega^\omega[0]=0\) which I don't know how to fix.
 * \(\textrm{lv}(0)=0\)
 * \(\textrm{lv}(\alpha+1)=\textrm{lv}(\alpha)\)
 * \(\textrm{lv}(\alpha)=\textrm{min}\{\beta|\beta>\textrm{lv}(\gamma),\alpha>\gamma\}\)
 * \(\alpha[0]=\textrm{min}\{\beta|\textrm{lv}(\beta)=\textrm{lv}(\alpha)-1\}\) if \(\textrm{lv}(\alpha)\) is a successor ordinal
 * \(\alpha[n+1]=\textrm{min}\{\beta|\textrm{lv}(\beta)=\textrm{lv}(\alpha)-1,\beta>\alpha[n]\}\) if \(\textrm{lv}(\alpha)\) is a successor ordinal
 * \(\alpha[n]=\textrm{min}\{\beta|\textrm{lv}(\beta)=\textrm{lv}(\alpha)[n]\}\) if \(\textrm{lv}(\alpha)\) is a limit ordinal