Borel sets without perfectly many overlapping translations IV
Tom 177 / 2024
Colloquium Mathematicum 177 (2024), 99-126
MSC: Primary 03E35; Secondary 03E15, 03E50
DOI: 10.4064/cm9104-12-2024
Opublikowany online: 8 January 2025
Streszczenie
We show that, consistently, there exists a Borel set admitting a sequence \langle \eta _\alpha :\alpha \lt \lambda \rangle of distinct elements of {}^{\omega }2 such that (\eta _\alpha +B)\cap (\eta _\beta +B) is uncountable for all \alpha ,\beta \lt \lambda but with no perfect set P such that |(\eta +B)\cap (\nu +B)|\geq 6 for any distinct \eta ,\nu \in P. This answers two questions from our previous works.
