User blog comment:Edwin Shade/Questions About Madore's Psi Function/@comment-26454151-20180110015756

4. The strength or size of Mahlo cardinals cannot be expressed in terms of fixed points, just like how the inaccessibles cannot be expressed in terms of fixed points. In fact, since inaccessibles cannot be proven to exist in ZFC, you can't describe the inaccessibles using only the techniques ZFC makes available (including fixed point enumerations). It is the same for Mahlo cardinals.