# 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)

Bib entry

@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} }