User blog comment:Deedlit11/Ordinal Notations V: Up to a weakly Mahlo cardinal/@comment-11227630-20140818113703

A few questions:

What do you mean "βth α-weakly inaccessible cardinal" for limit α or β?

For example, what's ωth weakly inaccessible cardinal? Since the limit of $$I,I_2,I_3,\cdots$$ has cofinality ω, it's not a weakly inaccessible. Is that ordinal represented by $$I_\omega$$ or $$\psi_{I_\omega}(0)$$ (or something else)?