Internally club and approachable for larger structures

John Krueger¹

¹ Department of Mathematics University of California Berkeley, CA 94720, U.S.A.

Fundamenta Mathematicae, Tome 201 (2008) no. 2, pp. 115-129

Résumé

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.

Détail

DOI : 10.4064/fm201-2-2

Keywords: generalize notion fat subset regular cardinal kappa fat subset kappa where kappa subseteq suppose kappa kappa supercompact there generic extension which kappa regular lambda there stationarily many lambda which internally club internally approachable