# Algebra Seminar talk

2022-05-20

Rahman **Mohammadpour***The universality problem for trees*

Abstract:

A weak embedding between two (infinite, usually uncountable)
trees is a function which preserves strict orders.
This induces a quasi-order over the class of trees.

The universality problem for a class of trees asks whether there is a universal tree in that class, i.e., a tree which weakly embeds all other members. I will talk about this quasi-order on some well-known classes of trees, and mention the known results and some open problems.