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 |