User blog comment:Denis Maksudov/Slowly growing ordinal function and FS up to BHO./@comment-28606698-20170404220238

The definition was rewritten as follows: 1) the first uncountable ordinal was included in set C_0, 2) in set C_n the operation of addition admitted for countable and uncountable ordinals, but only uncountable ordinal can be exponentiated (although both countable and uncountable ordinals can be exponent of uncountable ordinal), the multiplication operation is allowed if the first of the factors is an uncountable ordinal. So we slowed the growth of the function since $$\psi'(\Omega)=\varepsilon_0$$, but 1) it allows to express any non-zero ordinal since $$\psi'(0)=1$$ not $$\varepsilon_0$$ 2) it allows to simplify system of rules for assignation of fundamental sequences since we need not special rules for description FS for ordinals obtained by exponentiation of omega.