Global square and mutual stationarity at the ℵn

We give the proof of a theorem of Jensen and Zeman on the existence of a global □ sequence in the Core Model below a measurable cardinal κ of Mitchell order (oM(κ)) equal to κ++, and use it to prove the following theorem on mutual stationarity at ℵn.Let ω1 denote the first uncountable cardinal of V and set to be the class of ordinals of cofinality ω1. Theorem – If every sequence (Sn)n<ω of stationary sets , is mutually stationary, then there is an inner model with infinitely many inaccessibles (κn)n<ω so that for every mthe class of measurables λ with oM(λ)≥κm is, in V, stationary in κn for all n>m. In particular, there is such a model in which for all sufficiently large m<ω, the class of measurables λ with oM(λ)≥ωm is, in V, stationary below ℵm+2.