Borel sets without perfectly many overlapping translations IV
Abstract
We show that, consistently, there exists a Borel set B subset Cantor admitting a sequence (etaalpha:alpha<lambda) of distinct elements of Cantor such that (etaalpha+B) cap (etabeta+B) is uncountable for all alpha,beta<lambda but with no perfect set P such that |(eta+B) cap (nu+B)|>5 for any distinct eta,nu from P. This answers two questions from our previous works.
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