Logic Seminar: Isaac Goldbring (UC Irvine)

Theories of matrix ultraproducts

Answering a question of Farah, Hart, and Sherman, we show that the theories of matrix algebras do not converge.  In fact, we show that there are continuum many non-elementarily equivalent tracial ultraproducts of matrix algebras.  The proof uses ideas from finite group representation theory and definable groups in continuous logic.  This is joint work with Hiroshi Ando.