Mirna Dzamonja: Reasonable structures of size \(\aleph_1\)
13/05/22 08:27
Tuesday, May 17, 2022 17:00
Location: room 605, Mathematical Institute, University of Wroclaw
Speaker: Mirna Dzamonja (Université deParis-Cité)
Title: Reasonable structures of size \(\aleph_1\)
Abstract: We are interested to develop a theory of structures of size \(\aleph_1\) which are ’tame’ in the sense that they in some sense or other preserve the nice properties that we are used to seeing on the countable structures.
We explain the aim of the programme and then discuss a joint work with Wiesław Kubiś on a specific way of constructing structures of size \(\aleph_1\) using finite approximations, namely by organising the approximations along a simplified morass. We demonstrate a connection with Fraïssé limits and show that the naturally obtained structure of size \(\aleph_1\) is homogeneous. We give some examples of interesting structures constructed, such as a homogeneous antimetric space of size \(\aleph_1\). Finally, we comment on the situation when one Cohen real is added.
Location: room 605, Mathematical Institute, University of Wroclaw
Speaker: Mirna Dzamonja (Université deParis-Cité)
Title: Reasonable structures of size \(\aleph_1\)
Abstract: We are interested to develop a theory of structures of size \(\aleph_1\) which are ’tame’ in the sense that they in some sense or other preserve the nice properties that we are used to seeing on the countable structures.
We explain the aim of the programme and then discuss a joint work with Wiesław Kubiś on a specific way of constructing structures of size \(\aleph_1\) using finite approximations, namely by organising the approximations along a simplified morass. We demonstrate a connection with Fraïssé limits and show that the naturally obtained structure of size \(\aleph_1\) is homogeneous. We give some examples of interesting structures constructed, such as a homogeneous antimetric space of size \(\aleph_1\). Finally, we comment on the situation when one Cohen real is added.