Series: Penn State Logic Seminar

Date: Tuesday, April 3, 2001

Time: 2:30 - 3:20 PM

Place: 316 Willard Building

Speaker: Jeremy Avigad, Carnegie-Mellon University

Title: Between Proof Theory and Model Theory

Abstract: 

First, I will discuss the general proof theoretic goal of proving
conservation theorems, which provide a way of comparing axiomatic
theories and measuring their strength.  Then I will introduce a
model-theoretic notion, that of an Herbrand saturated model, and show
that this notion provides a smooth and uniform way of proving a number
of important conservation results.  In contrast to syntactic methods,
the model-theoretic methods just mentioned are nonconstructive: they
show that proofs in one theory can be translated to proofs in another,
without providing an explicit translation.  In the last part of this
talk, I will show how algebraic forcing methods can be used to render
the model-theoretic arguments constructive.