User blog comment:Bubby3/Psi function type I and II comparison./@comment-32467027-20170718085718/@comment-28606698-20170718132649

if Bubby is keeping in mind this definition then $$\psi_\nu(\alpha)$$ is the smallest ordinal that does not belong to set of all ordinals which can be generated from ordinals  less than $$\Omega_\nu$$ by the functions + (addition) and $$\psi_\mu(\eta)$$, where $$\mu<\omega$$ and $$\eta<\alpha$$.

$$\omega$$ is the smallest ordinal greater than all the positive integers i.e. smallest number with cardinality $$\aleph_0$$.

$$\Omega_\alpha$$ is $$\alpha$$-th uncountable ordinal i.e. smallest number with cardinality $$\aleph_\alpha$$ where $$\alpha>0$$.