PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

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