Abstract

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 $\nu \in C$ is inaccessible in the ground model. Unlike the forcing used by Gitik. the iterated forcing $R_{\lambda +1}$ used in this paper has the property that if λ is a cardinal less then κ then $R_{\lambda + 1}$ can be factored in V as $R_{\kappa + 1} = R_{\lambda + 1} \times R_{\lambda + 1, \kappa}$ where $\mid R_{\lambda +1}\mid \leq \lambda^+$ and $R_{\lambda + 1, \kappa}$ does not add any new subsets of λ