Logic Seminar
Christian Rosendal
UIC
Solution to Christensen's problem on universally measurable homomorphisms
Abstract: Answering a problem originating in J.P.R. Christensen's seminal work on Haar null sets, we show that a universally measurable homomorphism between Polish groups is automatically continuous.
Using our general analysis of continuity of group homomorphisms, this result is used to calibrate the consistency strength of the existence of a discontinuous homomorphism between Polish groups. In particular, it is shown that, modulo ZF+DC, the existence of a discontinuous homomorphism between Polish groups implies that the Hamming graph on Cantor space has finite chromatic number.
Tuesday September 11, 2018 at 3:30 PM in 427 SEO