October 2023
Aleksander Cieślak: Cofinalities of tree ideals and Shrinking Property
30/10/23 10:37
Tuesday, October 31, 2023 17:00
Location: room 601, Mathematical Institute, University of Wroclaw
Speaker: Aleksander Cieślak
Title: Cofinalities of tree ideals and Shrinking Property
Abstract: If \(\mathcal{T}\) is a collection of trees on \(\omega^\omega\), then we define the tree ideal \(t_0\) as a collection of these \(X\subset \omega^\omega\) such that each \(T\in \mathcal{T}\) has a subtree \(S\in \mathcal{T}\) which shares no branches with \(X\). We will be interested in the cofinalities of the tree ideals. In particular, we will focus on the condition, called "Incompatibility Shrinking Property", which implies that \(cof(t_0)>\mathfrak c\). We will consider under what assumptions this property is satisfied for the two types of trees, which are Laver and Miller trees which split positively according to some fixed ideal on \(\omega\).
Location: room 601, Mathematical Institute, University of Wroclaw
Speaker: Aleksander Cieślak
Title: Cofinalities of tree ideals and Shrinking Property
Abstract: If \(\mathcal{T}\) is a collection of trees on \(\omega^\omega\), then we define the tree ideal \(t_0\) as a collection of these \(X\subset \omega^\omega\) such that each \(T\in \mathcal{T}\) has a subtree \(S\in \mathcal{T}\) which shares no branches with \(X\). We will be interested in the cofinalities of the tree ideals. In particular, we will focus on the condition, called "Incompatibility Shrinking Property", which implies that \(cof(t_0)>\mathfrak c\). We will consider under what assumptions this property is satisfied for the two types of trees, which are Laver and Miller trees which split positively according to some fixed ideal on \(\omega\).
Maciej Korpalski: Straightening almost chains into barely altenating ones
23/10/23 10:34
Tuesday, October 24, 2023 17:00
Location: room 601, Mathematical Institute, University of Wroclaw
Speaker: Maciej Korpalski
Title: Straightening almost chains into barely altenating ones
Abstract: Consider an almost chain \(\mathcal{A} = \{A_x \subset \omega: x \in X\}\) for some separable linearly ordered set \(X\). Such a chain is barely alternating if for all \(n \in \omega\) we cannot find elements \(x_1 < x_2 < x_3 < x_4\) in \(X\) satisfying \(n \in A_{x_1}, A_{x_3}\), \(n \notin A_{x_2}, A_{x_4}\). We will show that under \(MA(\kappa)\), if \(|X| \leq \kappa\), then we can straighten our almost chain \(\mathcal{A}\) into a barely alternating one by changing at most finitely many elements in each set \(A_x\).
Location: room 601, Mathematical Institute, University of Wroclaw
Speaker: Maciej Korpalski
Title: Straightening almost chains into barely altenating ones
Abstract: Consider an almost chain \(\mathcal{A} = \{A_x \subset \omega: x \in X\}\) for some separable linearly ordered set \(X\). Such a chain is barely alternating if for all \(n \in \omega\) we cannot find elements \(x_1 < x_2 < x_3 < x_4\) in \(X\) satisfying \(n \in A_{x_1}, A_{x_3}\), \(n \notin A_{x_2}, A_{x_4}\). We will show that under \(MA(\kappa)\), if \(|X| \leq \kappa\), then we can straighten our almost chain \(\mathcal{A}\) into a barely alternating one by changing at most finitely many elements in each set \(A_x\).
Viktoriia Brydun: Monad on FMS(•) (Fuzzy Metric Spaces Category)
16/10/23 10:33
Tuesday, October 17, 2023 17:00
Location: room 601, Mathematical Institute, University of Wroclaw
Speaker: Viktoriia Brydun (Ivan Franko Lviv National University)
Title: Monad on FMS(•) (Fuzzy Metric Spaces Category)
Abstract: Monad on FMS(•) (Fuzzy Metric Spaces Category)
Location: room 601, Mathematical Institute, University of Wroclaw
Speaker: Viktoriia Brydun (Ivan Franko Lviv National University)
Title: Monad on FMS(•) (Fuzzy Metric Spaces Category)
Abstract: Monad on FMS(•) (Fuzzy Metric Spaces Category)
Arturo Martinez: Cardinal invariants related to free sets
09/10/23 10:23
Tuesday, October 10, 2023 17:00
Location: room 601, Mathematical Institute, University of Wroclaw
Speaker: Arturo Martinez
Title: Cardinal invariants related to free sets
Abstract: (Joint work with T. Żuchowski) Given a function \(f\) without fixed points, an infinite set \(A\) is called free for \(f\) if \(f[A] \cap A = \emptyset\). In this talk we will discuss some cardinal invariants related to families of free sets and we will discuss their relation between some cardinal invariants related to category and measure.
Location: room 601, Mathematical Institute, University of Wroclaw
Speaker: Arturo Martinez
Title: Cardinal invariants related to free sets
Abstract: (Joint work with T. Żuchowski) Given a function \(f\) without fixed points, an infinite set \(A\) is called free for \(f\) if \(f[A] \cap A = \emptyset\). In this talk we will discuss some cardinal invariants related to families of free sets and we will discuss their relation between some cardinal invariants related to category and measure.