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In V, assume that N ω is a strong limit cardinal and 2 Nω = N ω+1 . Let A be the set of approachable ordinals less than N ω+1 . An open question of M. Foreman is whether A can be non-stationary in some N ω and N ω+1 preserving extension of V. It is shown here that if W is such an outer model, then { k < ω: cf W (N V k ) = N W n } is infinite, for each positive integer n.

Cofinality changes required for a large set of unapproachable ordinals below $\aleph _{\omega +1}$