User blog comment:JHeroJr/Why I need a system that inductively defines set theories for each ordinal/@comment-35470197-20200109233744/@comment-35470197-20200110035903

> I guess I didn't expect it to work first try. I had no reason to believe such a fundamental sequence exists for every ordinal.

If you do not know ordinals well, then it is good to study them before trying studying hirgher order formal logic, because it is much more complicated.

> Can you give me an example of a non-zero limit ordinal that has no smallest fundamental sequence?

A non-zero limit ordinal has the smallest fundamental sequence if and only if it is ω.