User blog comment:Deedlit11/Ordinal Notations VI: Up to a weakly compact cardinal/@comment-11227630-20131105084532/@comment-11227630-20131106055708

Inaccessible mahlo cardinals are mahlo cardinals take on inaccessible arrays like M(1,w,0,0,w+1). Similarly, if mahlo cardinals take on mahlo diagonalizers, they're mahlo mahlo, or 1-mahlo such as Ξ(3,1).

If compact cardinals take on inaccessible arrays they're inaccessible compact, and if compact cardinals take on mahlo diagonalizers they're mahlo compact. And a compact compact cardinal diagonalizes all the (α@β)-mahlo compact cardinals just as a mahlo mahlo cardinal diagonalizes all the (α@β)-inaccessible mahlo cardinals(or M(α@β)).