User:Ynought/My ordinal notation

xi notation
This function takes an ordinal \(\alpha\) and turns it into a different ordinal

Attempt 1
\(\Phi\alpha\) means either \(\Omega_\alpha\) or \(\beta^\alpha\) where \(\beta\) is any ordinal or \(\alpha\times\beta\) or \(\alpha+\beta\) or it could be just \(\alpha\)

\(\alpha[n]\) is the n-th term in the fundamental sequence of \(\alpha\)

\(\xi(\Phi\alpha+1)[n]=\xi(\Phi\alpha)\uparrow\uparrow n\)se

\(\xi(\Phi\alpha)[n]=\xi(\Phi\alpha[n])\) if the previous case does not apply

\(\xi(\Phi\Omega)[n]=\text{sup}(\xi(\Phi\omega),\xi(\Phi\omega+\xi(\Phi\omega)),\xi(\Phi\omega+\xi(\Phi\omega+\xi(\Phi\omega)))...)\)