2025/12/24 by Pedro Marun, Marun, Pedro, Saharon shelah +3
Mathematics · Computer Science · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Advanced Banach Space Theory
paper · doi:10.48550/arxiv.2512.21247
We contribute to the study of ℵ1-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 \textsfMA that there exists an ℵ1-dense set of reals A so that, in any cardinal-preserving generic extension by a forcing of size ℵ1, 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.