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Hurewicz's property and concentrated sets in the Laver model

Speaker(s)
Piotr Szewczak
Affiliation
Cardinal Stefan Wyszynski University in Warsaw
Language of the talk
English
Date
May 21, 2025, 4:15 p.m.
Room
room 5050
Seminar
Topology and Set Theory Seminar

Let X be a set of reals. The set X is Hurewicz if for any sequence of countable increasing open covers of X one can select a single element from each cover such that the family of picked sets is a point-cofinite cover of X. The set X is b-concentrated, if X has size at least b and contains a countable set D such that each closed subset of X, disjoint with D, has size smaller than the bounding number b. Various types of concentrated sets play an important role in investigations related to products of sets with combinatorial covering properties.

 

By a recent result of Repovs and Zdomskyy, in the Laver model, Hurewicz sets have a specific form providing that the Hurewicz property is preserved by finite products in this model. The aim of the talk is to discuss a combinatorial structure of b-concentrated Hurewicz sets in the Laver model.

 

This is a joint work with Lyubomyr Zdomskyy.

 

The research was funded by the Polish National Science Center and Austrian Science Fund; Grant: Weave-UNISONO, Project: Set-theoretic aspects of topological selections

2021/03/Y/ST1/00122.