Not so many non-disjoint translations
Andrzej Roslanowski, Vyacheslav Rykov
TL;DR
This paper demonstrates the existence of a Borel set with uncountably many highly non-disjoint translations, yet lacking a perfect set of such translations, highlighting complex translation properties in descriptive set theory.
Contribution
It constructs a Borel set with uncountably many non-disjoint translations without a perfect set of them, revealing new insights into translation structures.
Findings
Existence of a Borel set with uncountably many non-disjoint translations
Such sets do not necessarily contain a perfect set of translations
Advances understanding of translation properties in descriptive set theory
Abstract
We show that, consistently, there is a Borel set which has uncountably many pairwise very non-disjoint translations, but does not allow a perfect set of such translations.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Rings, Modules, and Algebras · Mathematical Dynamics and Fractals