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

Title: | A survey of basis theorems. |

Seminar: | Logic Seminar |

Speaker: | Stephen G. Simpson, Pennsylvania State University |

Abstract: |

By a basis theorem I mean a theorem of the following form: Every nonempty effectively closed set in an effectively compact metric space contains at least one point which is, in a specific sense, close to being computable. Some well known basis theorems are: the Low Basis Theorem, the Hyperimmune-Free Basis Theorem, the R.E. Basis Theorem, and the Cone Avoidance Basis Theorem. Less well known are some recent basis theorems concerning propagation of randomness and partial randomness. In this talk we shall state some of these basis theorems and sketch their proofs. We shall also discuss the possibilities for combining these basis theorems in various ways. Some new results will be presented. |

### Room Reservation Information

Room Number: | MB315 |

Date: | 07 / 31 / 2012 |

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