Sh:1272

• Marun, P., Shelah, S., & Switzer, C. BAUMGARTNER-S AXIOM AND SMALL POSETS. Preprint. arXiv: 2512.21247
• Abstract:
  We contribute to the study of \aleph_1-dense sets of reals, a mainstay in set theoretic research since Baumgartner’s seminal work in the 70s. In particular, we show that it is consistent with \textsf{MA} that there exists an \aleph_1-dense set of reals A so that, in any cardinal-preserving generic extension by a forcing of size \aleph_1, A and A^* do not contain uncountable subsets which are order isomorphic. This strengthens a result of Avraham and the second author and yields a different proof of a theorem of Moore and Todorcevic.
• Version 2025-12-24_2 (10p)

@article{Sh:1272,
 author = {Marun, Pedro and Shelah, Saharon and Switzer, Corey},
 title = {{BAUMGARTNER-S AXIOM AND SMALL POSETS}},
 note = {\href{https://arxiv.org/abs/2512.21247}{arXiv: 2512.21247}},
 arxiv_number = {2512.21247}
}