Borel sets without perfectly many overlapping translations
Logic
2018-06-19 v1
Abstract
For a cardinal lambda<lambda_{omega_1} we give a ccc forcing notion P which forces that for some Borel subset B of the Cantor space (1) there a sequence (eta_alpha:alpha<lambda) of distinct elements such that |(eta_alpha+B) cap (eta_beta+B)|>5 for all alpha,beta<lambda, but (2) there is no perfect set of such eta's. The construction closely follows the one from Shelah math.LO/9802134
Keywords
Cite
@article{arxiv.1806.06283,
title = {Borel sets without perfectly many overlapping translations},
author = {Andrzej Roslanowski and Saharon Shelah},
journal= {arXiv preprint arXiv:1806.06283},
year = {2018}
}