Define NS_ω1 to be ω₂-saturated if there is no sequence of stationary sets, S_α for α<ω₂, such that S_α∩S_β is non-stationary for distinct α,β < ω₂.

Assume that NS_ω1 is ω₂-saturated and force with it to obtain a V-generic filter G. Then,

• if M is the Mostowski collapse of ult(V,G), then M is transitive,
• if j is the natural elementary embedding of V into M, then

  j(ω₁^V) = ω₁^M = ω₁^V[G] = ω₂^V

• M is countably closed in V[G]