- New
-
Topics
- All Categories
- Metaphysics and Epistemology
- Value Theory
- Science, Logic, and Mathematics
- Science, Logic, and Mathematics
- Logic and Philosophy of Logic
- Philosophy of Biology
- Philosophy of Cognitive Science
- Philosophy of Computing and Information
- Philosophy of Mathematics
- Philosophy of Physical Science
- Philosophy of Social Science
- Philosophy of Probability
- General Philosophy of Science
- Philosophy of Science, Misc
- History of Western Philosophy
- Philosophical Traditions
- Philosophy, Misc
- Other Academic Areas
- Journals
- Submit material
- More
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
My notes
Similar books and articles
On the axiom of extensionality in the positive set theory.Olivier Esser - 2003 - Mathematical Logic Quarterly 49 (1):97-100.
On Interpretability in the Theory of Concatenation.Vítězslav Švejdar - 2009 - Notre Dame Journal of Formal Logic 50 (1):87-95.
Interpretability over peano arithmetic.Claes Strannegård - 1999 - Journal of Symbolic Logic 64 (4):1407-1425.
Interpretability of Robinson arithmetic in the ramified second-order theory of dense linear order.A. P. Hazen - 1991 - Notre Dame Journal of Formal Logic 33 (1):101-111.
A cut-free sequent system for the smallest interpretability logic.Katsumi Sasaki - 2002 - Studia Logica 70 (3):353-372.
Interpretability over peano arithmetic.Claes Strannegård - 1999 - Journal of Symbolic Logic 64 (4):1407-1425.
Weak Theories of Concatenation and Arithmetic.Yoshihiro Horihata - 2012 - Notre Dame Journal of Formal Logic 53 (2):203-222.
Quantum Mathematics.J. Michael Dunn - 1980 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980:512 - 531.
The interpretability logic of peano arithmetic.Alessandro Berarducci - 1990 - Journal of Symbolic Logic 55 (3):1059-1089.
Comparing Peano arithmetic, Basic Law V, and Hume’s Principle.Sean Walsh - 2012 - Annals of Pure and Applied Logic 163 (11):1679-1709.
Cardinal arithmetic in the style of Baron Von münchhausen.Albert Visser - 2009 - Review of Symbolic Logic 2 (3):570-589.
Finite sets and natural numbers in intuitionistic TT without extensionality.Daniel Dzierzgowski - 1998 - Studia Logica 61 (3):417-428.
Interpretability degrees of finitely axiomatized sequential theories.Albert Visser - 2014 - Archive for Mathematical Logic 53 (1-2):23-42.
Analytics
Added to PP
2018-02-18
Downloads
41 (#379,234)
6 months
8 (#342,364)
2018-02-18
Downloads
41 (#379,234)
6 months
8 (#342,364)
Historical graph of downloads
Author's Profile
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.
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.
PhilPapers logo by Andrea Andrews and Meghan Driscoll.
This site uses cookies and Google Analytics (see our terms & conditions for details regarding the privacy implications). Use of this site is subject to terms & conditions.
All rights reserved by The PhilPapers Foundation
Server: philpapers-web-7c76586df8-pp8v9 uwo