Series: Penn State Logic Seminar
Date: Tuesday, November 25, 2003
Time: 2:30 - 3:45 PM
Place: 113 McAllister Building
Speaker: Carl Mummert, Penn State University, Mathematics
Title: An Incompleteness Theorem for beta_n-Models
Abstract:
Let omega denote the set of natural numbers, and P(omega) the
powerset of omega. For n a positive integer, a beta_n-model is a
subset of P(omega) which is a Sigma^1_n-elementary submodel of
P(omega). In this talk I will discuss recent joint work with
Stephen Simpson. The main result is a beta_n-model version of
G"odel's Second Incompleteness Theorem: if a recursively axiomatized
theory T has a beta_n-model, then so does T + ``there is no
countable beta_n-model of T.'' I will discuss several corollaries
of this theorem, including (1) the existence of a beta_n model which
is not a beta_{n+1} model, (2) a beta_n-model version of L"ob's
Theorem. This talk should be accessible to graduate students who
have taken a course in mathematical logic.
Mathematical Logic at Penn State
Department of Mathematics