Logic Seminar

A Polish module is a topological module whose underlying topology is Polish. In this talk, I will discuss some very recent work (joint with Forte Shinko) where we study when uncountable Polish modules continuously inject into one another and the pre-order induced by these injections. In particular we will show that, for a wide class of rings, there are countably many minimal elements in this pre-order. As an application, we will construct a countable family of uncountable abelian Polish groups, at least one of which embeds into any other uncountable abelian Polish group.