| A Gitik iteration with nearly Easton factoring (2003) | |||||||||||
Abstract | |||||||||||
| We reprove Gitik’s theorem that if the GCH holds and $o(\gk)=\gk+1$ then there is a generic extension in which $\gk$ is still measurable and there is a closed unbounded subset C of $\gk$ such that every $ν\in C$ is inaccessible in the ground model. Unlike the forcing used by Gitik, the iterated forcing $\radin\gl+1$ used in this paper has the property that if $\gl$ is a cardinal less then $\gk$ then $\radin\gl+1$ can be factored in V as $\radin\gk+1=\radin\gl+1\times\radin\gl+1,\gk$ where $\card{\radin\gl+1}\le\gl+$ and $\radin\gl+1,\gk$ does not add any new subsets of $\gl$. | |||||||||||
Publication details | |||||||||||
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