Internally club and approachable for larger structures
Volume 201 / 2008
Fundamenta Mathematicae 201 (2008), 115-129
MSC: 03E05, 03E35.
DOI: 10.4064/fm201-2-2
Abstract
We generalize the notion of a fat subset of a regular cardinal $\kappa $ to a fat subset of $P_{\kappa }(X)$, where $\kappa \subseteq X$. Suppose $\mu < \kappa $, $\mu ^{<\mu } = \mu $, and $\kappa $ is supercompact. Then there is a generic extension in which $\kappa = \mu ^{++}$, and for all regular $\lambda \ge \mu ^{++}$, there are stationarily many $N$ in $[H(\lambda )]^{\mu ^+}$ which are internally club but not internally approachable.
