Internally club and approachable for larger structures

Volume 201 / 2008

John Krueger Fundamenta Mathematicae 201 (2008), 115-129 MSC: 03E05, 03E35. DOI: 10.4064/fm201-2-2


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.


  • John KruegerDepartment of Mathematics
    University of California
    Berkeley, CA 94720, U.S.A.

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