Universally meager sets in the Miller model and similar ones

Speaker(s)

Piotr Szewczak

Affiliation

Cardinal Stefan Wyszynski University in Warsaw

Language of the talk

Polish

Date

Dec. 3, 2025, 4:15 p.m.

Room

room 4050

Title in English

Universally meager sets in the Miller model and similar ones

Seminar

Topology and Set Theory Seminar

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A subset X of the Cantor cube 2^\omega is universally meager, if every Borel isomorphic image of X is meager in 2^\omega.
We prove that in the Miller model and in a model constructed by Goldstern--Judah--Shelah all universally meager sets have size at most \omega_1.
Some relations between combinatorial covering properties in these models allow to obtain the same limitations for sizes of Rothberger and Hurewicz sets of reals with no homeomorphic copy of the Cantor set inside. 
This is a joint work with Valentin Haberl and Lyubomyr Zdomskyy.
The research was funded by the National Science Center, Poland Weave-UNISONO call in the Weave programme
Project: Set-theoretic aspects of topological selections 2021/03/Y/ST1/0012

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