Algebra Seminar talk
The universality problem for trees
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.