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

Title: | Cone Avoidance for Ramsey's theorem for pairs |

Seminar: | Logic Seminar |

Speaker: | Keita Yokoyama, Tokyo Institute of Technology and Pennsylvania State University |

Abstract: |

Determining the strength of Ramsey's theorem for pairs (RT^2_2) is a
long standing problem in Computability Theory and Reverse Mathematics.
The following two theorems are the significant contributions to this problem.
In 1990s, Seetapun proved the cone avoidance theorem for Ramsey's
theorem for pairs, which implies that RT^2_2 is strictly weaker than
ACA_0.
In 2001, Cholak, Jockusch and Slaman constructed a low_2 omega-model
of RT^2_2 by using Mathias forcing, and showed that the first-order
part of RT^2_2 is weaker than the system of Sigma_2-induction.
In this talk, I will introduce another proof of Seetapun's theorem
given by Dzhafarov and Jockusch, which is based on Mathias forcing
used for the latter theorem. |

### Room Reservation Information

Room Number: | MB315 |

Date: | 11 / 29 / 2011 |

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