March 2023
Tomasz Zuchowski: Katětov order on Borel ideals
28/03/23 12:22
Tuesday, March 28, 2023 17:00
Location: room A.4.1 C-19
Speaker: Tomasz Zuchowski
Title: Katětov order on Borel ideals
Abstract: An ideal \(\mathcal{I}\) on \(\omega\) is Katětov reducible to ideal \(\mathcal{J}\) if there is a function \(f:\omega\to \omega\) such that if \(I\in\mathcal{I}\) then \(f^{-1}[I]\in\mathcal{J}\). The existence of such reduction is related to some cardinal invariants and other properties of considered ideals. We will present some examples of Borel ideals with or without Katětov reductions between them. Furthermore we will prove a structural dichotomy about Katětov order for all Borel ideals.
The presented results are from the paper “Katětov order on Borel ideals” by Michael Hrusak.
Location: room A.4.1 C-19
Speaker: Tomasz Zuchowski
Title: Katětov order on Borel ideals
Abstract: An ideal \(\mathcal{I}\) on \(\omega\) is Katětov reducible to ideal \(\mathcal{J}\) if there is a function \(f:\omega\to \omega\) such that if \(I\in\mathcal{I}\) then \(f^{-1}[I]\in\mathcal{J}\). The existence of such reduction is related to some cardinal invariants and other properties of considered ideals. We will present some examples of Borel ideals with or without Katětov reductions between them. Furthermore we will prove a structural dichotomy about Katětov order for all Borel ideals.
The presented results are from the paper “Katětov order on Borel ideals” by Michael Hrusak.
Sebastian Jachimek: Combinatorial Banach spaces
16/03/23 17:29
Tuesday, March 21, 2023 17:00
Location: room A.4.1 C-19
Speaker: Sebastian Jachimek
Title: Combinatorial Banach spaces
Abstract: Combinatorial space is a type of Banach space induced by (some) family of sets in a certain way. During the talk I will present examples of families (of subsets of natural numbers) and spaces related with them. Furthermore, I will consider properties of these spaces, in particular in the context of containing isomorphic copy of \(c_0\) and \(\ell_1\).
Location: room A.4.1 C-19
Speaker: Sebastian Jachimek
Title: Combinatorial Banach spaces
Abstract: Combinatorial space is a type of Banach space induced by (some) family of sets in a certain way. During the talk I will present examples of families (of subsets of natural numbers) and spaces related with them. Furthermore, I will consider properties of these spaces, in particular in the context of containing isomorphic copy of \(c_0\) and \(\ell_1\).
Grzegorz Plebanek: Countable extensions of compact lines
09/03/23 20:47
Tuesday, March 14, 2023 17:00
Location: room A.2.22 C-19
Speaker: Grzegorz Plebanek
Title: Countable extensions of compact lines
Abstract: For a compact space \(K\), we say that \(L\) is a countable discrete extension of \(K\) if \(L\) is compact and consists of \(K\) and a countable set of isolated points. We investigate some properties of such extenions for separable compact lines \(K\). This is directly related to properties of almost chains of subsets of \( \mathbb{N}\).
Location: room A.2.22 C-19
Speaker: Grzegorz Plebanek
Title: Countable extensions of compact lines
Abstract: For a compact space \(K\), we say that \(L\) is a countable discrete extension of \(K\) if \(L\) is compact and consists of \(K\) and a countable set of isolated points. We investigate some properties of such extenions for separable compact lines \(K\). This is directly related to properties of almost chains of subsets of \( \mathbb{N}\).
Aleksander Cieślak: Trees and Cohen reals
01/03/23 08:02
Tuesday, March 7, 2023 17:00
Location: room A.2.22 C-19
Speaker: Aleksander Cieślak
Title: Trees and Cohen reals
Abstract: We will discuss adding Cohen reals for various types of trees on Baire and Cantor space. We will distinguish that these Cohen reals can be added in a 'strong' or 'weak' way. While the former has rather pathological consequences, the latter allows certain control over the ideal related to the tree type.
Location: room A.2.22 C-19
Speaker: Aleksander Cieślak
Title: Trees and Cohen reals
Abstract: We will discuss adding Cohen reals for various types of trees on Baire and Cantor space. We will distinguish that these Cohen reals can be added in a 'strong' or 'weak' way. While the former has rather pathological consequences, the latter allows certain control over the ideal related to the tree type.