Sh:1187

• Rosłanowski, A., & Shelah, S. (2025). Borel sets without perfectly many overlapping translations, III. Ann. Pure Appl. Logic, 176(6), Paper No. 103565, 49. arXiv: 2009.03471 DOI: 10.1016/j.apal.2025.103565 MR: 4874855
• Abstract:
  We expand the results of Rosłanowski and Shelah [RoSh:1138,RoSh:1170] to all Abelian Polish groups (H,+). We show that under the Martin Axiom, if \aleph_\alpha<{\mathfrak c}, \alpha<\omega_1 and 4\leq\iota<\omega, then there exists a \Sigma^0_2 set B\subseteq H which has \aleph_\alpha many pairwise \iota–nondisjoint translations but not a perfect set of such translations.
• Version 2021-07-28 (47p) published version (49p)

@article{Sh:1187,
 author = {Ros{\l}anowski, Andrzej and Shelah, Saharon},
 title = {{Borel sets without perfectly many overlapping translations, III}},
 journal = {Ann. Pure Appl. Logic},
 fjournal = {Annals of Pure and Applied Logic},
 volume = {176},
 number = {6},
 year = {2025},
 pages = {Paper No. 103565, 49},
 issn = {0168-0072},
 mrnumber = {4874855},
 mrclass = {03E35 (03E15 03E50 20K45 54H05)},
 doi = {10.1016/j.apal.2025.103565},
 note = {\href{https://arxiv.org/abs/2009.03471}{arXiv: 2009.03471}},
 arxiv_number = {2009.03471}
}