User blog comment:Alemagno12/Defining stage n cardinals in terms of stationary sets/@comment-5529393-20180611195103/@comment-25601061-20180611213749

1. Fixed.

2. I noticed the following pattern: (let fixed point operations be operations cardinals with some ordinal property X -> cardinals with some ordinal property Y that are limits of cardinals with some ordinal property X )

Judging by the fact that Ξ(K,0) is a hyper-Mahlo and the fact that KOCF doesn't collapse greatly Mahlos to avoid ruining the correspondence between indescribables and Πn-reflection, this lead me to believe that if we diagonalized over repeated application and diagonalization of the fixed point operation over and over again starting with the ordinal property of being the first x-Mahlo for some x, it could get us to weakly compacts
 * A Mahlo cardinal is an inaccessible which is stationary over the set of inaccessibles below it, and it diagonalizes repeated application and diagonalization of the fixed point operation over and over again starting with inaccessibility
 * A 1-Mahlo cardinal is a Mahlo which is stationary over the set of Mahlos below it, and it diagonalizes repeated application and diagonalization of the fixed point operation over and over again starting with Mahloness
 * A 2-Mahlo cardinal is a 1-Mahlo which is stationary over the set of Mahlos below it, and it diagonalizes repeated application and diagonalization of the fixed point operation over and over again starting with 1-Mahloness