User blog comment:Nayuta Ito/faketest/e0/@comment-30754445-20180805015451/@comment-32697988-20180805095603

Let me explain how I understood Mahlos in UNOCF.

There is a function ψM.

ψM(0) is defined to be Ω.

ψM(α+1) is defined to be Ωβ+1 when ψM(α)=Ωβ.

ψM(α), when α is a limit ordinal but cof(α)≠M, makes ψ(ψM(α)) into ψ(ψcof(α)(ψM(α)), and it nests ψcof(α).

ψM(α), when cof(α)=M, is a bit complicated. First, define function f to be the function that replaces the last M in α with the input, and calculate it's first fixed point. (It's like the OCF up to BHO). For example, for ψM(M2), you get the ordinal ψM(M×ψM(M×ψM(M×ψM(M×...)))). Call this β. Then, ψM(α) is the ordinal γ　that satisfies ψγ(γ)=β.

For example, from the first three rules, we can know that ψM(α)=Ω1+α if α<M. Then, β=ψM(M) has satisfy "ψβ(β) is the 1st fixed point of γ→ψM(γ)". The 1st fixed point of γ→ψM(γ) is the omega fixed point ΩΩ Ω Ω ... , which equals to ψI(I) in UNOCF, so ψM(M)=I.

I find UNOCF to be more newbie-friendly because in Deedlit's Mahlo OCF he uses χ function which is, in my opinion, hard to understand.