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.