English

MA$_{\omega_1}(S)[S]$ does not imply $\mathcal{K}_2$

Logic 2022-09-23 v2

Abstract

We construct a model in which MAω1_{\omega_1}(S)[S] holds and K2\mathcal{K}_2 fails. This shows that MAω1_{\omega_1}(S)[S] does not imply K2\mathcal{K}_2 and answers an old question of Larson and Todorcevic in [3]. We also investigate different strong colorings in models of MAω1_{\omega_1}(S)[S].

Keywords

Cite

@article{arxiv.2208.14896,
  title  = {MA$_{\omega_1}(S)[S]$ does not imply $\mathcal{K}_2$},
  author = {Yinhe Peng and Liuzhen Wu},
  journal= {arXiv preprint arXiv:2208.14896},
  year   = {2022}
}