User blog:Alemagno12/Defining stage n cardinals in terms of stationary sets

Let: Then, we have that: Further, if we extend the S function to S(TT,x) and beyond:
 * S(0,0) = I
 * S(α+1,x) = the (1+x)th cardinal such that it is of the form S(α,y) and the set of cardinals of the form S(α,y) less than it is stationary in it
 * S(α+Tβ+1,x) = the (1+x)th cardinal such that it is of the form S(α+Tβy,0) and the set of cardinals of the form S(α+Tβy,0) less than it is stationary in it
 * Else, S(α,x) = sup{y|y=S(β,x)∧β<α}
 * S(0,x) enumerates the inaccessibles
 * S(1,x) enumerates the Mahlos
 * S(1+y,x) enumerates the y-Mahlos
 * S(T,x) enumerates the weakly compacts
 * S(T2,x) enumerates the stage 4 cardinals
 * S(Ty,x) enumerates the stage 2+x cardinals
 * S(TT,x) enumerates the Π12-indescribables
 * S(TT T ,x) enumerates the Π13-indescribables
 * S(T↑↑y,x) enumerates the Π1y-indescribables
 * S(εT+1,x) enumerates the Π1ω-indescribables = Π20-indescribables