MUTUAL INTERPRETABILITY OF ROBINSON ARITHMETIC AND ADJUNCTIVE SET THEORY WITH EXTENSIONALITY

An elementary theory of concatenation, QT(+), is introduced and used to establish mutual interpretability of Robinson arithmetic, Minimal Predicative Set Theory, quantifier-free part of Kirby's finitary set theory, and Adjunctive Set Theory, with or without extensionality. The most basic arithmetic and simplest set theory thus turn out to be variants of string theory.