Series: Logic Seminar
Time: Wednesday, March 4, 1998, at 1:25 PM
Place: 121 Thomas Building
Speaker: Juliette Kennedy (Bucknell)
Title: On Embedding Models of Arithmetic into Reduced Products
Abstract:
In the early 1970's Tennenbaum proved that all countable models of
PA^- (the elementary theory of the nonnegative parts of discretely
ordered rings) which are Diophantine correct are present up to
isomorphism in the reduced power of the natural numbers modulo the
cofinite filter. This theorem raises the question of when any function
from the natural numbers to the natural numbers can belong to a model
of arithmetic inside the reduced power. We give a partial solution to
this question, which is related to Skolem's 1934 construction of a
non-standard model of arithmetic. We will also present an analogue of
the MRDP theorem, given in terms of the componentwise behavior of
integer-valued functions.