Open Colorings and Baumgartner's Axiom
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.
Fields of Study & Subjects
Advanced Topology and Set Theory
Computability
Logic
AI Algorithms
Advanced Banach Space Theory
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 3 January 2026
- Document type
- Preprint