User blog:PsiCubed2/How to make Deedlit's Mahlo-level notation more intuitive

Replace all instances of χ(a,b) with I(M×a+b)...

And that's it!

Now we have a new collapsing function I which - as it's name implies - keeps track of our inaccessible acrdinals in a very straight forward manner:

I(n) = In

I(M) = I(1,0)

I(M2) = I(1,0,0)

I(M3×5+M2×I+M×Γ₀+7) = I(5,I,Γ₀,7) = I(5,I(1),Γ₀,7)

I(Mω×5+M3×Γ₀+7) = I(1@ω, Γ₀@3, 7@0)

Of-course, once we reach I(MM), this I function stops looking like an extended Veblen function, and starts looking like a full-fledged collapsing function. So:

I(MM) = I(MI(M I(M ...) ) )

and so on.