User blog comment:Edwin Shade/Understanding The Infinite/@comment-32213734-20171110205605

Here are my thoughts about common fixed points.

They are basically for limit α. For successor α+1, I think, Rule 2 may be simplified:

φα+1(β) is equal to the 1+βth fixed point of the function φα(γ) = γ

(it should be also fixed points for all ordinals < α by this definition)

But for a limit ordinal, say, ω, we have not predecessor, so, we should use common fixed points:

φω(β) is 1+βth common fixed point of all functions φn(γ) = γ, n is natural number

By the way, shouldn't in Rule 2 be γ ↦ φδ(γ) instead of γ ↦ φδ(α)?