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arXiv · 2009.03471

Borel sets without perfectly many overlapping translations, III

Andrzej Roslanowski·Saharon Shelah
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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 $α<ω_1$ and $4\leq k<ω$, then there is a ccc forcing notion adding a $Σ^0_2$ set $B\subseteq H$ which has $\aleph_α$ many pairwise $k$--overlapping translations but not a perfect set of such translations.

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Andrzej Roslanowski, Saharon Shelah. 2021-08-03. Borel sets without perfectly many overlapping translations, III. https://arxiv.org/abs/2009.03471

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