Mathematical logic seminar – Oct 9 2018

Time: 3:30pm – 4:30 pm

Room: Wean Hall 8220

Speaker: Clinton Conley

Department of Mathematical Sciences

CMU

Title: Realizing abstract systems of congruence II

Abstract:

An abstract system of congruence (ASC) is simply an equivalence relation

on the power set of a finite set F satisfying some nondegeneracy

conditions. Given such an ASC and an action of a group G on a set X, a

realization of the ASC is a partition of X into pieces indexed by F such

that whenever two subsets A, B are asc-equivalent, the corresponding

subsets XA and XB of X can be translated to one another in the action.

Familiar notions like paradoxical decompositions can be easily formalized

and refined by the ASC language. Wagon, upon isolating this notion,

characterized those ASCs which can be realized by rotations of the sphere.

He asks whether there is an analogous characterization for realizing ASCs

using partitions with the property of Baire. We provide such a

characterization. This is joint work with Andrew Marks and Spencer Unger.