# Meeting Details

Title: Neutral measures, continuous degrees, and the Brouwer fixed point theorem Logic Seminar Stephen G. Simpson, Pennsylvania State University http://www.math.psu.edu/simpson/ Let [0,1] be the unit interval. A neutral measure is a probability measure N on [0,1] such that every real number in [0,1] is random with respect to N. The existence of neutral measures was first proved by L. Levin. We present a simple proof of the existence of neutral measures using the Brouwer fixed point theorem. We use Miller's theory of continuous degrees to prove the following: for any neutral measure N there exists a PA-complete Turing degree which is reducible to N.

### Room Reservation Information

Room Number: MB315 04 / 20 / 2010 02:30pm - 03:45pm