Sh:1138

• Rosłanowski, A., & Shelah, S. (2019). Borel sets without perfectly many overlapping translations. Rep. Math. Logic, (54), 3–43. arXiv: 1806.06283 DOI: 10.4467/20842589rm.19.001.10649 MR: 4011916
• Abstract:
  For a cardinal \lambda<\lambda_{\omega_1} we give a ccc forcing notion P such that in V^P there is a \Sigma^0_2 set B\subseteq {}^\omega 2 with a sequence \langle\eta_\alpha: \alpha<\lambda\rangle of distinct elements of {}^\omega 2 such that \big|(\eta_\alpha+B)\cap (\eta_\beta+B)\big|\geq 6 for all \alpha,\beta<\lambda but does not have a perfect set of such \eta’s. The construction closely follows the one from [Sh:522, Section 1].
• Version 2018-06-16_11 (25p) published version (41p)

@article{Sh:1138,
 author = {Ros{\l}anowski, Andrzej and Shelah, Saharon},
 title = {{Borel sets without perfectly many overlapping translations}},
 journal = {Rep. Math. Logic},
 fjournal = {Reports on Mathematical Logic},
 number = {54},
 year = {2019},
 pages = {3--43},
 issn = {0137-2904},
 mrnumber = {4011916},
 mrclass = {03E15 (03E35 03E50)},
 doi = {10.4467/20842589rm.19.001.10649},
 note = {\href{https://arxiv.org/abs/1806.06283}{arXiv: 1806.06283}},
 arxiv_number = {1806.06283}
}