Characterizations of interpretability in bounded arithmetic
Logic
2016-02-02 v1
Abstract
This paper deals with three tools to compare proof-theoretic strength of formal arithmetical theories: interpretability, -conservativity and proving restricted consistency. It is well known that under certain conditions these three notions are equivalent and this equivalence is often referred to as the Orey-H\'ajek characterization of interpretability. In this paper we look with detail at the Orey-H\'ajek characterization and study what conditions are needed and in what meta-theory the characterizations can be formalized.
Cite
@article{arxiv.1602.00555,
title = {Characterizations of interpretability in bounded arithmetic},
author = {Joost J. Joosten},
journal= {arXiv preprint arXiv:1602.00555},
year = {2016}
}