Mutual Interpretability of Robinson Arithmetic and Adjunctive Set Theory with Extensionality

TL;DR

This paper demonstrates that Robinson arithmetic and various set theories, including Adjunctive Set Theory with extensionality, are mutually interpretable using an elementary theory of concatenation, highlighting their foundational connections.

Contribution

It introduces an elementary theory of concatenation to establish mutual interpretability among several foundational theories in logic and set theory.

Findings

Robinson arithmetic is interpretable in Adjunctive Set Theory

Adjunctive Set Theory can interpret Robinson arithmetic

Mutual interpretability holds with or without extensionality

Abstract

An elementary rheory of concatenation is introduced and used to establish mutual interpretability of Robinson arithmetic, Minimal Predicative Set Theory, the quantifier-free part of Kirby's finitary set theory, and Adjunctive Set Theory, with or without extensionality.