For more information about this meeting, contact Stephen Simpson.

Title: | Measure-theoretic regularity: logical aspects. |

Seminar: | Logic Seminar |

Speaker: | Stephen G. Simpson, Pennsylvania State University |

Abstract Link: | http://www.math.psu.edu/simpson/papers/massmtr.pdf |

Abstract: |

Let S be a Lebesgue measurable set in Euclidean space. It is well known that if S is of positive measure, then S includes a closed set of positive measure. In fact, given epsilon > 0, we can find a closed set C included in S such that the measure of S minus the measure of C is less then epsilon. This phenomenon is known as measure-theoretic regularity. In this talk we examine the foundational or metamathematical aspects of measure-theoretic regularity. We quantify the "descriptive complexity" or "logical strength" of the closed sets which are needed in order to implement measure-theoretic regularity at various levels of the Borel hierarchy. |

### Room Reservation Information

Room Number: | MB315 |

Date: | 09 / 08 / 2009 |

Time: | 02:30pm - 03:45pm |