Characterizations of interpretability in bounded arithmetic

Joost J. Joosten

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arXiv · 1602.00555

Characterizations of interpretability in bounded arithmetic

Joost J. Joosten

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Abstract

This paper deals with three tools to compare proof-theoretic strength of formal arithmetical theories: interpretability, $Π^0_1$-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-Hájek characterization of interpretability. In this paper we look with detail at the Orey-Hájek characterization and study what conditions are needed and in what meta-theory the characterizations can be formalized.

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BibTeX RIS

Joost J. Joosten. 2016-02-01. Characterizations of interpretability in bounded arithmetic. https://arxiv.org/abs/1602.00555

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