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

Title: | The reverse mathematics of Peano categoricity |

Seminar: | Logic Seminar |

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

Abstract: |

We define a system to be an ordered triple A,f,i where A is a set, f is a function from A to A, and i is a distinguished element of A. We say that the system A,f,i is inductive if A is the only subset of A which is closed under f and contains i. We define a Peano system to be an inductive system such that f is one-to-one and i does not belong to the range of f. A key theorem in the foundations of mathematics due to Dedekind (1888) asserts that every Peano system is isomorphic to the standard Peano system N,S,1 where N is the set of positive integers and S(n) = n+1 for all n in N. We investigate the question of which axioms are needed to prove Dedekind's theorem. Our investigation is carried out in the context of reverse mathematics. We show for instance that Dedekind's theorem is logically equivalent to WKL0 over RCA0*, and from this result we draw some foundational/philosophical insights. This is joint work with Keita Yokoyama. Our paper is available on-line at
http://www.math.psu.edu/simpson/papers/rmpc.pdf . |

### Room Reservation Information

Room Number: | MB315 |

Date: | 09 / 25 / 2012 |

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