User blog comment:Wythagoras/All my stuff/@comment-7484840-20130715121715/@comment-5529393-20130715144000

The iota function is really the ultimate breaking of the gentleman's rule, by co-opting all other defined functions!

Anyway, it is always possible to beat a function. The iota function cannot use all functions;  for example it cannot use another function that is defined similarly to iota that dominates all "legal" functions. Call the functions that iota can use type 0. The iota function and similar functions can be called type 1 functions. We can then define a type 2 function that dominates all type 1 functions, a type 3 function that dominates all type 2 functions, etc. We can continue this to arbitrarily high ordinals.