Bulletin of Symbolic Logic

A Model-Theoretic Approach to Ordinal Analysis

Jeremy Avigad and Richard Sommer

Full-text is available via JSTOR, for JSTOR subscribers. Go to this article in JSTOR.

Abstract

We describe a model-theoretic approach to ordinal analysis via the finite combinatorial notion of an α-large set of natural numbers. In contrast to syntactic approaches that use cut elimination, this approach involves constructing finite sets of numbers with combinatorial properties that, in nonstandard instances, give rise to models of the theory being analyzed. This method is applied to obtain ordinal analyses of a number of interesting subsystems of first- and second-order arithmetic.

Article information

Source
Bull. Symbolic Logic Volume 3, Number 1 (1997), 17-52.

Dates
First available in Project Euclid: 20 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.bsl/1182353487

Mathematical Reviews number (MathSciNet)
MR1444913

Zentralblatt MATH identifier
0874.03068

JSTOR
links.jstor.org

Citation

Avigad, Jeremy; Sommer, Richard. A Model-Theoretic Approach to Ordinal Analysis. Bull. Symbolic Logic 3 (1997), no. 1, 17--52.https://projecteuclid.org/euclid.bsl/1182353487


Export citation