User blog comment:Rgetar/Creating FGH for transfinite ordinals/@comment-35470197-20190630215635/@comment-35470197-20190630235906

I meant a recursion in arithmetic. You can create a recursive system of fundamental sequences for recursive ordinals using an ordinal notation only using arithmetic, which is much simpler than set theory, but it is really difficult to create a similar system for uncountable ordinals because you essentially need non-trivial transcendental induction in set theory.