English

Adding cofinal countable sequences through multiple regular cardinals by ssp forcing

Logic 2025-10-29 v1

Abstract

We present a direct construction of stationary set preserving forcings that make ω\omega-cofinal all the members of some arbitrary set K\mathcal{K} of regular cardinals κ>ω1\kappa > \omega_1. In addition, it is made possible to ensure that no other uncountable regular cardinals from the ground model acquire countable cofinality in the forcing extension. Our method is elementary, being based on a combinatorial argument by Foreman and Magidor together with generalizations of typical side-condition arguments and needs no assumptions beyond ZFC\mathsf{ZFC}.

Keywords

Cite

@article{arxiv.2510.24634,
  title  = {Adding cofinal countable sequences through multiple regular cardinals by ssp forcing},
  author = {Ben De Bondt and Boban Velickovic},
  journal= {arXiv preprint arXiv:2510.24634},
  year   = {2025}
}

Comments

15 pages

R2 v1 2026-07-01T07:09:57.605Z