PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Stephen Simpson, Jan Reimann.

Title:Explicit and implicit definability over the integers, part 1
Seminar:Logic Seminar
Speaker:Stephen G. Simpson, Pennsylvania State University
Abstract:
We begin with a discussion of implicit and explicit definability in general, mentioning Beth's Definability Theorem. We then specialize to definability over the ring of integers. (So now we are talking about what recursion theorists call arithmetical sets versus arithmetical singletons.) The main part of the talk consists of three examples. Example 1: a set X which is implicitly definable but not explicitly definable. Namely, X = the Tarski truth set for arithmetic. Example 2: an implicitly definable pair of sets X, Y such that Y by itself is not implicitly definable. Namely, X = the Tarski truth set and Y = a set which is explicitly definable from X and Cohen-generic for arithmetic. Example 3: a pair of sets X, Y such that X is implicitly definable, Y is implicitly definable, X is not explicitly definable from Y, and Y is not explicitly definable from X. This is an unpublished result of Leo Harrington.

Room Reservation Information

Room Number:MB315
Date:11 / 27 / 2012
Time:02:30pm - 03:45pm