 
Summary: The ModelTheoretic Ordinal Analysis of
Theories of Predicative Strength
Jeremy Avigad and Richard Sommer
October 14, 1997
Abstract
We use modeltheoretic methods described in [3] to obtain ordinal
analyses of a number of theories of first and secondorder arithmetic,
whose prooftheoretic ordinals are less than or equal to 0.
1 Introduction
In [3] we introduced a modeltheoretic approach to ordinal analysis
as an interesting alternative to cut elimination. Here we extend these
methods to the analysis of stronger theories of first and secondorder
arithmetic which are nonetheless predicatively justifiable.
When used in this sense, the word "predicative" refers to a foun
dational stance under which one is willing to accept the set of natural
numbers as a completed totality, but not the set of all subsets of the
natural numbers. In this spirit, predicative theories bar definitions that
require quantification over the full power set of N, depicting instead
a universe of sets of numbers that is constructed "from the bottom
up." Work of Feferman and Sch¨utte has established that the ordinal
