A Gitik iteration with nearly Easton factoring

We reprove Gitik’s theorem that if the GCH holds and o(κ) = κ + 1 then there is a generic extension in which κ is still measurable and there is a closed unbounded subset C of κ such that every ν ∈ C is inaccessible in the ground model. Unlike the forcing used by Gitik, the iterated forcing Rλ+1 used in this paper has the property that if λ is a cardinal less then κ then Rλ+1 can be factored in V as Rκ+1 = Rλ+1 ×Rλ+1,κ where |Rλ+1| ≤ λ and Rλ+1,κ does not add any new subsets of λ. §