User blog comment:Wythagoras/FGH of Dollar Function new version/@comment-11227630-20131109131352/@comment-11227630-20131110013027

Well, just as I think, maybe the diagonalizer of Ξ3 function is the "compact compact compact" cardinal. Now pay attention to the subscript of Ξ - it means multiple-ex-compact cardinal. But what about the fixed point that α->Ξα(1,0), which is (1,0)-ex-compact cardinal?

However, it's a long way below the thing after inaccessibles, mahlos and compacts. In your page I see C1 are mahlos, C2 are compacts, and C3 will be the "stage-4-things". I think the subscript of your ordinal notation means the "stage function", but what about bringing a diagonalizer of that stage function?