# Meeting Details

For more information about this meeting, contact Stephen Simpson.

Title: LR-reducibility and the Turing jump operator Logic Seminar Stephen G. Simpson, Pennsylvania State University http://www.math.psu.edu/simpson/papers/massmtr.pdf For any recursive ordinal alpha, let 0^(alpha) denote the alpha-th Turing jump of 0. We prove that if 0^(alpha) is LR-reducible to a Turing oracle X then 0^(alpha+1) is Turing reducible to the Turing jump of X. We then apply this result to the study of measure-theoretic regularity in the effective Borel hierarchy. In particular, 0^(alpha) is LR-reducible to X if and only if every set at level alpha+2 of the effective Borel hierarchy includes a set of the same measure which is an effective union of effectively closed sets relative to X.

### Room Reservation Information

Room Number: MB315 11 / 10 / 2009 02:30pm - 03:45pm