Authors
Jeremy Avigad
Carnegie Mellon University
Abstract
An approach to ordinal analysis is presented which is finitary, but highlights the semantic content of the theories under consideration, rather than the syntactic structure of their proofs. In this paper the methods are applied to the analysis of theories extending Peano arithmetic with transfinite induction and transfinite arithmetic hierarchies.
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References found in this work BETA

On the Scheme of Induction for Bounded Arithmetic Formulas.A. J. Wilkie & J. B. Paris - 1987 - Annals of Pure and Applied Logic 35 (3):261-302.
Elementary Descent Recursion and Proof Theory.Harvey Friedman & Michael Sheard - 1995 - Annals of Pure and Applied Logic 71 (1):1-45.
First-Order Proof Theory of Arithmetic.Samuel R. Buss - 2000 - Bulletin of Symbolic Logic 6 (4):465-466.
Subsystems of Set Theory and Second-Order Number Theory.Wolfram Pohlers - 2000 - Bulletin of Symbolic Logic 6 (4):467-469.

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Citations of this work BETA

Saturated Models of Universal Theories.Jeremy Avigad - 2002 - Annals of Pure and Applied Logic 118 (3):219-234.

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