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arXiv · 2208.14896

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

Yinhe Peng·Liuzhen Wu
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Abstract

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

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Yinhe Peng, Liuzhen Wu. 2022-08-31. MA$_{\omega_1}(S)[S]$ does not imply $\mathcal{K}_2$. https://arxiv.org/abs/2208.14896

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