English

Universal countably chromatic graph

Logic 2025-11-12 v1

Abstract

We show that the existence of a universal countably chromatic graph of size 1\aleph_1 together with the failure of continuum hypothesis is consistent. The proof is a forcing iteration of strongly proper ccc posets. The construction works for any uncountable successor cardinal κ+\kappa^+, where κ\kappa is regular.

Keywords

Cite

@article{arxiv.2511.07608,
  title  = {Universal countably chromatic graph},
  author = {Siiri Kivimäki},
  journal= {arXiv preprint arXiv:2511.07608},
  year   = {2025}
}
R2 v1 2026-07-01T07:30:49.563Z