Sh:1259

• Mildenberger, H., & Shelah, S. FORCING DIAMOND AND APPLICATIONS TO ITERABILITY. Preprint.
• Abstract:
  We show that higher Sacks forcing at a regular limit cardinal and club Miller forcing at an uncountable regular cardinal both add a diamond sequence. We answer the longstanding question, whether \kappa = \kappa^{<\kappa} \geq\aleph_1 implies that \kappa-supported iterations of \kappa-Sacks forcing do not collapse \kappa^+ and are \kappa-proper in the affirmative. The results pertain to other higher tree forcings.
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@article{Sh:1259,
 author = {Mildenberger, Heike and Shelah, Saharon},
 title = {{FORCING DIAMOND AND APPLICATIONS TO ITERABILITY}}
}