Borel sets without perfectly many overlapping translations, II

2019/09/03 by Andrzej Rosłanowski, Saharon Shelah, Roslanowski, Andrzej +1
Computer Science · Mathematics · #03E15 #03E35 #03E50 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1909.00937

openalex publication_date 2019/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a countable ordinal epsilon we construct a Sigma⁰₂ subset of the Cantor space for which one may force aleph_epsilon translations with intersections of size 2i, but such that it has no perfect set of such translations in any ccc extension. These sets have uncountably many translations with intersections of size 2i in ZFC, so this answers Problem 3.4 of arxiv:1711.04058 .

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