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 \(\omega\).