Sh:1259

• Mildenberger, H., & Shelah, S. FORCING DIAMOND AND APPLICATIONS TO ITERABILITY. Preprint. arXiv: 2504.08390
• 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.
• Version 2025-04-09 (27p)

@article{Sh:1259,
 author = {Mildenberger, Heike and Shelah, Saharon},
 title = {{FORCING DIAMOND AND APPLICATIONS TO ITERABILITY}},
 note = {\href{https://arxiv.org/abs/2504.08390}{arXiv: 2504.08390}},
 arxiv_number = {2504.08390}
}