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arXiv:2208.14896 [math.LO]AbstractReferencesReviewsResources

MA$_{ω_1}(S)[S]$ does not imply $\mathcal{K}_2$

Yinhe Peng, Liuzhen Wu

Published 2022-08-31Version 1

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].

Categories: math.LO
Subjects: 03E02, 03E35, 03E65
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