Sh:1191

• Mildenberger, H., & Shelah, S. Higher Miller forcing may collapse cardinals. J. Symbolic Logic. To appear.
• 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.
• Version 2021-10-28 (27p) published version (24p)

@article{Sh:1191,
 author = {Mildenberger, Heike and Shelah, Saharon},
 title = {{Higher Miller forcing may collapse cardinals}},
 journal = {J. Symbolic Logic},
 year = {to appear}
}