User blog comment:Wythagoras/Dollar function: final version/@comment-11227630-20131118112531

What about using the "stage function" and the diagonalizer of the "stage function" here to descirbe large cardinals? If we use S(α,β) to represent the (1+β)-th stage-α cardinal, and use T for diagonalizer of S function in the first argument, (and S(α,0)=S(α)) we'll get S(1)=I, S(2)=M, S(3)=K, S(w) is the first ordinal in the ω-th row, S(T) is the first ordinal in the second plane, S(T2) is the first ordinal in the third plane, S(T^2) is the first ordinal in the second cube, S(T^ω) is the limit of n-dimension. And there will be S(T^S(T)), S(T^T), S(T^T^T), S(e(T+1)), ...