English

Derived Models in PFA

Logic 2025-07-21 v2

Abstract

We discuss a conjecture of Wilson that under the proper forcing axiom, Θ0\Theta_0 of the derived model at κ\kappa is below κ+\kappa^+. We prove the conjecture holds for the old derived model. Assuming mouse capturing in the new derived model, the conjecture holds there as well. We also show Θ<κ+\Theta < \kappa^+ in the case of the old derived model, and under additional hypotheses for the new derived model.

Keywords

Cite

@article{arxiv.2501.05954,
  title  = {Derived Models in PFA},
  author = {Derek Levinson and Nam Trang},
  journal= {arXiv preprint arXiv:2501.05954},
  year   = {2025}
}
R2 v1 2026-06-28T21:02:35.900Z