User blog comment:Ikosarakt1/Fast-growing hierarchy/@comment-7484840-20130620190007/@comment-7484840-20130622112934

The 'any ordinal structure' means any combination of ordinals ending in this case, an Omega, for example z0e0*w+Omega.

The last 3 rules are supposed to be a shorter way of writing the rules defining how to evaluate an Omega within the theta function.