User blog comment:Edwin Shade/In Which I Try To Derive Values of Madore's OCF on My Own, and See How Far I Get/@comment-32213734-20171203100352

Adding Ω in argument of Ψ increases  subscript of   ζ  by one.

Ψ(Ψ1(0)) = Ψ(εΩ + 1) = BHO = ζBHO

Ψ(Ψ1(0) + Ω) = ζBHO + 1 = ζΨ(ε Ω + 1) + 1

Ψ(Ψ1(Ω2)) = Ψ(ζΩ + 1)

or, in infinite number of cardinatities variation,

Ψ(Ω2) = Ψ(ζΩ + 1)

(See Ordinal collapsing function, Going beyond the Bachmann-Howard ordinal).