User blog comment:Deedlit11/Ordinal Notations V: Up to a weakly Mahlo cardinal/@comment-11227630-20140818113703/@comment-1605058-20140818130651

If I remember correctly, Deedlit once said that "b-th a-weakly inaccessible" can be replaced with "b-th a-weakly inaccessible or limit of such". This answers the question of b limit. If a is limit, then cardinal is a-weakly inaccessible if it's k-weakly inaccessible for all k<a.