English

Forcing $\mathbf{\Sigma}^1_1$-Separation on $\omega_1^{\omega_1}$

Logic 2026-05-21 v1

Abstract

We prove that it is consistent that every two disjoint boldface Σ11\mathbf{\Sigma}^1_1 subsets of ω1ω1\omega_1^{\omega_1} can be separated by a boldface Δ11\mathbf{\Delta}^1_1 set. The forcing starts from LL and preserves CH and therefore also ω1<ω1=ω1\omega_1^{<\omega_1}=\omega_1.

Cite

@article{arxiv.2605.21175,
  title  = {Forcing $\mathbf{\Sigma}^1_1$-Separation on $\omega_1^{\omega_1}$},
  author = {Stefan Hoffelner},
  journal= {arXiv preprint arXiv:2605.21175},
  year   = {2026}
}
R2 v1 2026-07-22T07:24:02.461Z