More on pseudoradial spaces

This talk is the second part of the `pseudoradial spaces'-series. We'll present a few more results on this topic, focusing on one that uses  Davies-trees. This concept was presented by Thomas last seminar.

A subset A of X is radially closed if there are no sequences (of any cardinal length) within A converging to X\A. The radial closure of a set A is the minimum radially closed set containing A. A space is pseudoradial if the radial closure of any subset is closed.

We will present a nice technique to produce convergent sequences in forcing extensions out of elementary submodels.