Reasonable structures of size aleph_1

Osoba referująca: 
Mirna Dzamonja (Université deParis-Cité)
wtorek, 17. Maj 2022 - 17:00
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 ℵ1 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 ℵ1 is homogeneous. We give some examples of interesting structures constructed, such as a homogeneous antimetric space of size ℵ1. Finally, we comment on the situation when one Cohen real is added. About 15 minutes before the seminar we invite you for coffee and a chat.