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Logic Seminar

Wednesday, September 2, 2020
12:00pm to 1:00pm
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A dichotomy for Polish modules
Joshua Frisch, Department of Mathematics, Caltech,

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.

For more information, please contact Math Department by phone at 626-395-4335 or by email at mathinfo@caltech.edu.