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Borel sets without perfectly many overlapping translations, III (2009.03471v2)
Published 8 Sep 2020 in math.LO
Abstract: We expand the results of Roslanowski and Shelah arXive:1806.06283 , arXive:1909.00937 to all perfect Abelian Polish groups $(H,+)$. In particular, we show that if $\alpha<\omega_1$ and $4\leq k<\omega$, then there is a ccc forcing notion adding a $\Sigma0_2$ set $B\subseteq H$ which has $\aleph_\alpha$ many pairwise $k$--overlapping translations but not a perfect set of such translations.