User blog comment:Moooosey/dco + decord sequence/@comment-35470197-20191009222350/@comment-35392788-20191010190555

Bear in mind that if you just want fundamental sequences up to some arbitrary point, you can require a given fundamental system \(\alpha[n] : \mu \inter \text{Lim} \times \mathbb{N} \to \mu\) that works up to some ordinal \(\mu\). Of course, this restricts the system to values below \(\mu\).

This is what the FGH does. The FGH is technically not well-defined without a given system of fundamental sequences, though it doesn't get brought up very often.