English

Open Colorings and Baumgartner's Axiom

Logic 2026-01-06 v1

Abstract

We construct a model of MA1+OCAT\mathsf{MA_{\aleph_1}}+\mathsf{OCA}_T where Baumgartner's Axiom fails, settling a question of Farah. Moreover, in the same model there is an 1\aleph_1-dense set of reals which is neither reversible nor increasing, answering a question of Marun, Shelah, and Switzer.

Keywords

Cite

@article{arxiv.2601.01166,
  title  = {Open Colorings and Baumgartner's Axiom},
  author = {Lorenzo Notaro},
  journal= {arXiv preprint arXiv:2601.01166},
  year   = {2026}
}

Comments

14 pages

R2 v1 2026-07-01T08:49:18.565Z