 
Summary: Formalizing Forcing Arguments in Subsystems of
SecondOrder Arithmetic
Jeremy Avigad
October 23, 1996
Abstract
We show that certain modeltheoretic forcing arguments involving sub
systems of secondorder arithmetic can be formalized in the base the
ory, thereby converting them to effective prooftheoretic arguments. We
use this method to sharpen conservation theorems of Harrington and
BrownSimpson, giving an effective proof that WKL+0 is conservative
over RCA0 with no significant increase in the lengths of proofs.
1 Introduction
Although forcing is usually considered to be a modeltheoretic technique it has
a prooftheoretic side as well, in that forcing notions can usually be expressed
syntactically in the base theory. One can often use this fact to convert a model
theoretic forcing argument to a prooftheoretic one, and in doing so obtain a
sharper and more effective version of the theorem being proven. We'll illustrate
this approach by formalizing two conservation results, one due to Harrington
and the other due to Brown and Simpson, involving subsystems of secondorder
arithmetic. These results orginally appeared in the author's dissertation [1],
