Adding cofinal countable sequences through multiple regular cardinals by ssp forcing

Abstract

We present a direct construction of stationary set preserving forcings that make $\ddot{I}‰$-cofinal all the members of some arbitrary set $\mathcal{K}$ of regular cardinals $\hat{I}º>\ddot{I}{‰}_1$. In addition, it is made possible to ensure that no other uncountable regular cardinals from the ground model acquire countable cofinality in the forcing extension. Our method is elementary, being based on a combinatorial argument by Foreman and Magidor together with generalizations of typical side-condition arguments and needs no assumptions beyond $\mathsf{ZFC}$.

15 pages