Borel sets without perfectly many overlapping translations

by Roslanowski and Shelah. [RoSh:1138]

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 < eta_alpha : alpha < lambda > of distinct elements of {}^omega 2 such that |(eta_alpha +B) cap (eta_beta +B) | >= 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].


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