Namba forcing singularizes the successor cardinal \(\aleph_2\), giving it cofinality \(\aleph_0\), without collapsing \(\aleph_1\). We exhibit a simple construction of a ground model with a regular cardinal \(\kappa\) over which there is a Namba-like forcing which gives \(\kappa^+\) cofinality \(\aleph_0\) without collapsing cardinals or cofinalities \(\leq \kappa\). The construction uses a measurable cardinal, and indeed covering arguments show that a measurable cardinal is necessary. We also discuss singularizations to cofinalities other than \(\aleph_0\) and singularizations of successors of singular cardinals. This is joint work with Dominik Adolf, Berkeley and Arthur Apter, CUNY.
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