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

Title: | Degrees of unsolvability: some recent results |

Seminar: | Logic Seminar |

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

Abstract: |

A mass problem is a set of reals. If P and Q are mass problems, we say that P is Muchnik reducible to Q if for each real y in Q there exists a real x in P such that x is Turing reducible to y. A Muchnik degree is an equivalence class of mass problems under mutual Muchnik reducibility. It is well known that the lattice of all Muchnik degrees provides a rigorous implementation of Kolmogorov's nonrigorous 1932 interpretation of intuitionism as a "calculus of problems" (Aufgabenrechnung). In this talk I will discuss some recent results concerning the sublattice consisting of the Muchnik degrees of nonempty, effectively closed sets of reals. |

### Room Reservation Information

Room Number: | MB315 |

Date: | 02 / 24 / 2015 |

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