English

An Iteration Theorem for $\omega_1$-preserving Forcings

Logic 2024-03-15 v1

Abstract

We prove an iteration theorem which guarantees for a wide class of nice iterations of ω1\omega_1-preserving forcings that ω1\omega_1 is not collapse, at the price of needing large cardinals to burn as fuel. More precisely, we show that a nice iteration of ω1\omega_1-preserving forcings which force SRP at successor steps and preserves old stationary sets does not collapse ω1\omega_1.

Keywords

Cite

@article{arxiv.2403.09018,
  title  = {An Iteration Theorem for $\omega_1$-preserving Forcings},
  author = {Andreas Lietz},
  journal= {arXiv preprint arXiv:2403.09018},
  year   = {2024}
}
R2 v1 2026-06-28T15:19:30.480Z