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.
• Version 2025-04-09 (27p)

@article{Sh:1259,
 author = {Mildenberger, Heike and Shelah, Saharon},
 title = {{FORCING DIAMOND AND APPLICATIONS TO ITERABILITY}}
}