A model-theoretic approach to ordinal analysis

Bulletin of Symbolic Logic 3 (1):17-52 (1997)
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.
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DOI 10.2307/421195
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Michael Rathjen (1994). Proof Theory of Reflection. Annals of Pure and Applied Logic 68 (2):181-224.
Jeremy Avigad (1996). On the Relationship Between ATR 0 And. Journal of Symbolic Logic 61 (3):768-779.
Richard Sommer (1995). Transfinite Induction Within Peano Arithmetic. Annals of Pure and Applied Logic 76 (3):231-289.

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