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explicitly definable from X. This is an unpublished result of Leo Harrington.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 |