User blog comment:Deedlit11/Ordinal Notations III: Collapsing Higher Cardinalities/@comment-7484840-20130706154845/@comment-10429372-20130706183722

Yes, that is true. Theta use same thing, but you can also use:

Theta(phi(2,Omega_2+1))  = Theta(e_(Omega_2)+1) = lim((Omega_2), (Omega_2)^(Omega_2), (Omega_2)^(Omega_2)^(Omega_2)...)

Theta(phi(2,Omega_2+1)) = lim((e_(Omega_2)+1), (e_(e_(Omega_2)+1)+1)...)

Theta(phi(w,Omega_2+1)) = lim(Theta(phi(1,Omega_2+1)), Theta(phi(2,Omega_2+1))...)

Theta(Omega_3) = Theta(Gamma_Omega_2) = lim(Theta(phi(w,Omega_2+1)), Theta(phi(Theta(phi(w,Omega_2+1),Omega_2+1)...)