Theories and ordinals in proof theory

Michael Rathjen

pp. 719-743

in: Proof-theoretic semantics, Synthese 148 (3), 2006.

Abstract

How do ordinals measure the strength and computational power of formal theories? This paper is concerned with the connection between ordinal representation systems and theories established in ordinal analyses. It focusses on results which explain the nature of this connection in terms of semantical and computational notions from model theory, set theory, and generalized recursion theory.