User blog comment:Deedlit11/Ordinal Notations VI: Up to a weakly compact cardinal/@comment-11227630-20131105084532/@comment-11227630-20131107025500

To LittlePeng9:

Ordinal α takes on inaccessible array, which means it takes on hyper-inaccessible cardinals based on α. e.g. I(1,0,0,w) is an inaccessible array based on I, and M(1,0,0,w) is an inaccessible array based on M, or I call it an inaccessible mahlo cardinal. What I(α@β) does to the ψ function is just what M(α@β) does to the χ function.

To Wythagoras:

It seems that the M2 works not so strong as I think. What I think originally is that M2 works as a diagonalizer of χ1 function just as Ω2 works as a diagonalizer of ψ1 function. And I(I(...I(M+1)))=ψI(1,M+1)(0), I(w,M+1)=χ1(w), I(M,1)=χ1(M), I(I(w,M+1),0)=χ1(χ1(w)), I(1,0,M+1)=χ1(M2).