User blog comment:Alemagno12/Defining stage n cardinals in terms of stationary sets/@comment-11227630-20180612011934

Using normal cardinal operations such as cardinal exponentiation, and getting next omega-fixed-point, getting fixed point of them, getting higher and higher fixed points, etc. - all those still can't get an inaccessible.

Similarly, getting such a cardinal that "α-Mahlo cardinals below it are stationary in it", getting fixed point of them, getting "x is x-Mahlo" (hyper-Mahlo), getting hyper-hyper-Mahlo, getting "x is hyperx-Mahlo", getting higher and higher Mahloness, etc. - all those still can't get a weakly compact.