User blog comment:LittlePeng9/Higher order set theory/@comment-10429372-20140926180316

Wait a sec... Doesn't Rayoα(n) grow at least gα(n)? (g is SGH).

It seems quite weird that it doesn't. Doesn't that mean that the growth rate is too high for FGH?

Also, there must be undefinable ordinals between w1CK and w1? These will be undefinable in OOST. I think that - and I know that I should be careful throwing this term around - that OOST growth rate is w1DEF. Also, would it be able to make (O+1)OST, which would diagonalize over all ordinals, i.e. define f(n) = OOST^n(n) and much higher functions?