Mathematical logic seminar – October 4 2016

Time: 3:30pm – 4:30 pm

Room: Wean Hall 8220

Speaker: Andy Zucker

Department of Mathematical Sciences

CMU

Title: Topological dynamics and Devlin’s theorem

Abstract:

If G is a topological group, a G-flow is a compact Hausdorff space X with a continuous right action a: X x G to X. A G-ambit is just a flow X along with a point x_0 in X whose orbit is dense. After a brief introduction to the world of G-flows and G-ambits, we will define a new dynamical object, a completion ambit, and discuss some of their basic properties. Of course, given any category of dynamical systems, it’s natural to ask whether the category has a universal object, and if so, if it is unique. Time permitting, we will connect these questions to a striking theorem of D. Devlin from his 1979 thesis about the partition properties of the countable dense linear order.