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arXiv · 2601.01166

Open Colorings and Baumgartner's Axiom

Lorenzo Notaro
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Abstract

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

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Lorenzo Notaro. 2026-01-03. Open Colorings and Baumgartner's Axiom. https://doi.org/10.1090/proc/17829

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