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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References found in this work BETA
Proof Theory of Reflection.Michael Rathjen - 1994 - Annals of Pure and Applied Logic 68 (2):181-224.
Formalizing Forcing Arguments in Subsystems of Second-Order Arithmetic.Jeremy Avigad - 1996 - Annals of Pure and Applied Logic 82 (2):165-191.
On the Relationship Between ATR 0 And.Jeremy Avigad - 1996 - Journal of Symbolic Logic 61 (3):768-779.
Transfinite Induction Within Peano Arithmetic.Richard Sommer - 1995 - Annals of Pure and Applied Logic 76 (3):231-289.
On the Relationships Between ATR0 and $\Widehat{ID}_{.Jeremy Avigad - 1996 - Journal of Symbolic Logic 61 (3):768 - 779.

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Saturated Models of Universal Theories.Jeremy Avigad - 2002 - Annals of Pure and Applied Logic 118 (3):219-234.
Some Variations of the Hardy Hierarchy.Henryk Kotlarski - 2005 - Mathematical Logic Quarterly 51 (4):417.

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