User blog comment:Vel!/Ultracardinals/@comment-5029411-20140619002153

Then H_2 is is second hyperultracardinal.

H_3 is is third hyperultracardinal.

H_H_H... is micro(H,W).

micro(H,W_2)

micro(H,W_w)

micro(H,W_W)

micro(H,I)

micro(H,U)

micro(H,H)

micro(H,H(1)2)

micro({LL...LLH,H}_{H,H}, where there is H L's)

M is megaultracardinal, which is the limit of all hyperultracardinals

G is gigaultracardinal, which is the limit of all megaultracardinals

We continue this. U(a,0) = U_a, U(a,1) = H_a, U(a,2) = M_a, U(a,3) = G_a, etc.

U(U,U)

U(U,U(1)2)

U({LL...LLU,U}_{U,U}, where there is U L's)

Limit of U is Z cardinal.