# Sh:1191

• Mildenberger, H., & Shelah, S. Higher Miller forcing may collapse cardinals. Preprint.
• Abstract:
We show that it is independent whether club-\kappa-Miller forcing preserves \kappa^{++}. We show that under \kappa^{<\kappa} > \kappa, club-\kappa-Miller forcing collapses some cardinal in [\kappa^+,\kappa^{<\kappa}] to \kappa. Answering a question by Brendle, Brooke-Taylor, Friedman and Montoya, we show that the iteration of ultrafilter \kappa-Miller forcing does not have the Laver property.
@article{Sh:1191,
}