For more information about this meeting, contact Stephen Simpson.

Title: | Mass problems and measure-theoretic regularity |

Seminar: | Logic Seminar |

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

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

Abstract: |

According to Y. Medvedev and A. Muchnik, a mass problem is a set of Turing oracles which are regarded as the "solutions" of the problem.
A mass problem is said to be weakly reducible to another mass problem if any "solution" of the second problem can be used as a Turing oracle to compute some "solution" of the first problem. For each recursive ordinal number alpha, we consider the problem B_alpha of regularizing sets at level alpha + 2 of the effective Borel hierarchy. Thus, to solve B_alpha means to find a countable union of closed sets included in a given set at level alpha + 2 which is of the same measure as the given set. We show that this problem is Sigma^0_3. From this it follows that this family of problems is embeddable in the lattice of weak degrees of mass problems associated with effectively closed sets in Euclidean space. |

### Room Reservation Information

Room Number: | MB315 |

Date: | 12 / 01 / 2009 |

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