PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Jan Reimann, Jason Rute, Stephen Simpson.

Title:Lebesgue density and \Pi^0_1 classes
Seminar:Logic Seminar
Speaker:Mushfeq Khan, University of Wisconsin - Madison
Abstract:
Analyzing the effective content of the Lebesgue density theorem was an important step towards the recent solutions of the ML-covering and ML-cupping problems. Two new classes of reals emerged from this analysis: the positive density points with respect to effectively closed (or \Pi^0_1) sets of reals, and a proper subclass, the density-one points. Bienvenu, Holzl, Miller, and Nies have shown that the ML-random positive density points are exactly the ones that do not compute the halting problem. Using this theorem as a starting point, I will discuss several new results on the interactions between density, domination properties, minimality, completeness, 1-genericity, and randomness.

Room Reservation Information

Room Number:MB315
Date:04 / 29 / 2014
Time:02:30pm - 03:45pm