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*Aleksander Cieślak*

Speaker:Speaker:

*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*Maciej Korpalski*

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*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*Viktoriia Brydun (Ivan Franko Lviv National University)*

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*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*Arturo Martinez*

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*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.