User blog comment:Deedlit11/Ordinal Notations V: Up to a weakly Mahlo cardinal/@comment-180.159.72.141-20160322163141/@comment-27513631-20160322170132

As far as I understand it, it means that you can't 'get' to the quality of being a weakly Mahlo cardinal by using what you used to get to a weakly inaccessible cardinal, which can also be used to get to a 1-weakly inaccessible, a hyper-weakly inaccessible, a \((1@\alpha)\)-weakly-inaccessible, and so on.