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Mutual interpretability of Robinson arithmetic and adjunctive set theory with extensionality
Bulletin of Symbolic Logic 23 (4):381-404 (2017)
Abstract
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.Author's Profile
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Citations of this work
The Enhanced Indispensability Argument, the circularity problem, and the interpretability strategy.Jan Heylen & Lars Arthur Tump - 2019 - Synthese 198 (4):3033-3045.
Intuitionistic sets and numbers: small set theory and Heyting arithmetic.Stewart Shapiro, Charles McCarty & Michael Rathjen - forthcoming - Archive for Mathematical Logic.
Internal Categoricity, Truth and Determinacy.Martin Fischer & Matteo Zicchetti - 2023 - Journal of Philosophical Logic 52 (5):1295-1325.
References found in this work
Concatenation as a basis for arithmetic.W. V. Quine - 1946 - Journal of Symbolic Logic 11 (4):105-114.
Growing Commas. A Study of Sequentiality and Concatenation.Albert Visser - 2009 - Notre Dame Journal of Formal Logic 50 (1):61-85.
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