English

Adding highly generic subsets of $\omega_2$

Logic 2023-08-25 v3

Abstract

Starting from the GCH,\rm{GCH}, we build a cardinal and GCH\rm{GCH} preserving generic extension of the universe, in which there exists a set Aω2A \subseteq \omega_2 of size 2\aleph_2 so that every countably infinite subset of AA or ω2A\omega_2 \setminus A is Cohen generic over the ground model.

Cite

@article{arxiv.2301.09435,
  title  = {Adding highly generic subsets of $\omega_2$},
  author = {Esfandiar Eslami and Mohammad Golshani and Rouholah Hoseini Naveh},
  journal= {arXiv preprint arXiv:2301.09435},
  year   = {2023}
}
R2 v1 2026-06-28T08:17:47.558Z