Universally meager sets in the Miller model and similar ones

Prelegent(ci)

Piotr Szewczak

Afiliacja

Cardinal Stefan Wyszynski University in Warsaw

Język referatu

polski

Termin

3 grudnia 2025 16:15

Pokój

p. 4050

Tytuł w języku angielskim

Universally meager sets in the Miller model and similar ones

Seminarium

Seminarium „Topologia i teoria mnogości”

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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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