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A Model-Theoretic Approach to Ordinal Analysis

Published online by Cambridge University Press:  15 January 2014

Jeremy Avigad  and
Richard Sommer
Jeremy Avigad
Affiliation:
Department of Philosophy, Carnegie Mellon University, Pittsburgh, PA 15213, USA, E-mail: avigad+@cmu.edu
Richard Sommer
Affiliation:
Department of Mathematics, Stanford University, Stanford, CA 94305-2125, USA, E-mail: sommer@math.stanford.edu
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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.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 3 , Issue 1 , March 1997 , pp. 17 - 52
Copyright
Copyright © Association for Symbolic Logic 1997

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