User blog comment:Wythagoras/Catching function in normal ordinals/@comment-11227630-20140203095754/@comment-1605058-20140626125809

What do you mean by "recursive way"? Do you mean defining fundamental sequences in fully recursive way (because this uniquely defines hierarchies and catching points)? This isn't possible.

Either way, as far as I know, no one has proved that catching function is partial in any instance of definition.