Date of Original Version
Reflections on the Foundations of Mathematics : Essays in Honor of Solomon Feferman. Edited by W. Sieg, R. Sommer, and C.L. Talcott. Lecture Notes in Logic 15, ASL Publications, A K Peters, 1-36, 2002.
Abstract or Table of Contents
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.