The interpretability logic of all reasonable arithmetical theories

TL;DR

This paper explores the interpretability logic of all reasonable arithmetical theories, examining both their arithmetical and modal aspects to understand their foundational properties.

Contribution

It provides a comprehensive analysis of the interpretability logic for a broad class of arithmetical theories, linking arithmetical and modal perspectives.

Findings

Established the connection between arithmetical theories and modal interpretability logic

Identified key properties of the interpretability logic for all reasonable theories

Presented a framework for analyzing interpretability in arithmetical theories

Abstract

This paper from 2000 is a presentation of a status qu{\ae}stionis at that tiime, to wit of the problem of the interpretability logic of {\em all}\/ reasonable arithmetical theories. We present both the arithmetical side and the modal side of the question.