PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Stephen Simpson.

Title:Mass problems associated with effectively closed sets
Seminar:Logic Seminar
Speaker:Stephen G. Simpson, Pennsylvania State University
We examine some specific degrees of unsolvability of mass problems associated with nonempty effectively closed sets in the Cantor space. It is known that these degrees of unsolvability form a countable distributive lattice with 0 and 1. This lattice is known as P_w. We show that the top degree 1 in P_w is associated with the problem of finding a completion of an effectively essentially undecidable theory. We characterize 1 abstractly up to recursive homeomorphism and up to Turing equivalence, in terms of properties of effectively closed sets. We also consider a certain degree r in P_w which is intermediate between 0 and 1. We characterize r as the degree of the problem of finding an infinite sequence of head and tails which is random in the sense of Martin-Loef. Alternatively, we characterize r as the maximum degree of an effectively closed set of positive measure. As time permits we shall exhibit other interesting examples of specific, natural degrees in P_w.

Room Reservation Information

Room Number:MB106
Date:11 / 06 / 2007
Time:02:30pm - 03:45pm