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

Title: | On the computability of rates of metastable convergence |

Seminar: | Logic Seminar |

Speaker: | Jason Rute, Penn State |

Abstract: |

There are many ways to express that a sequence converges. They range from the most explicit but least uniform---a rate of convergence; to the moderately explicit and moderately uniform---a bound on the number of jumps by epsilon; to the least explicit but most uniform---a bound of metastable convergence (which I will define in this talk).
Using proof theory, Kolhenbach showed that (under certain conditions) uniform metastable bounds can be computably extracted from the proof of a convergence theorem. Using model theory, Avigad and Iovino showed that (under similar conditions) metastable bounds of a convergence theorem are always uniform---but their methods do not provide a way to compute the bounds. Using computable analysis and computable model theory, I show that not only are the bounds always uniform, but they can computed from the statement of the theorem alone (without regards to the proof). |

### Room Reservation Information

Room Number: | MB315 |

Date: | 02 / 11 / 2014 |

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