User blog comment:Hyp cos/Attempt of OCF up to Stability/@comment-31580368-20181029042115

If I understand correctly S(1,0) means fisrt fixed point (x+α)-stable and equal λx.x-stable. How then to express sup((x+n)-stable|n<λx.x-stable)? Next... S(1,1) equal λx.x+1-stable S(2,0) equal λx.x*2-stable S(1,0,0) equal λx.x2-stable ... S(1,3,4,2,5) equal λx.x4+x3*3+x2*4+x*2+5-stable ... S(1,0,...) equal λx.xω-stable this is very similar to the Veblen hierarchy. And λx.xω-stable like SVO, then λx.xx ω -stable would be like like LVO. And so on, up to Bachman hierarchy (λx.εx+1-stable).

Can we use the diagonalizer (+)-stable to express this hierarchy?

And... In terms of the cardinals can we use n-subtle like S(n,0)?