Borel sets without perfectly many overlapping translations
Abstract
For a cardinal lambda<lambdaomega1 we give a ccc forcing notion P which forces that for some Borel subset B of the Cantor space (1) there a sequence (etaalpha:alpha<lambda) of distinct elements such that |(etaalpha+B) cap (etabeta+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
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