  The Noetherian type of a space X, Nt(X), is the least cardinal kappa such
that X has a base B such that every element of the base is contained in less
than kappa many elements of the base. Denote X the space obtained from
2^{aleph_omega} by declaring the G_delta sets to be open. Milovich proved that
if Square_{aleph_omega} holds and (aleph_omega)^omega=aleph_{omega+1} then
Nt(X)=omega_1. Answering a question of Spadaro, we show that if
(aleph_omega)^omega=aleph_{omega+1} and a strong form of Chang Conjecture holds
for aleph_\omega then Nt(X)>omega_1.
