# On Interpretability Between Some Weak Essentially Undecidable Theories

@article{Kristiansen2020OnIB, title={On Interpretability Between Some Weak Essentially Undecidable Theories}, author={Lars Kristiansen and Juvenal Murwanashyaka}, journal={Beyond the Horizon of Computability}, year={2020}, volume={12098}, pages={63 - 74} }

We introduce two essentially undecidable first-order theories \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {WT}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage…

## 3 Citations

### Weak essentially undecidable theories of concatenation

- Materials ScienceArchive for Mathematical Logic
- 2022

In the language {0,1,∘,⪯}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}…

### MUTUAL INTERPRETABILITY OF WEAK ESSENTIALLY UNDECIDABLE THEORIES

- Computer ScienceThe Journal of Symbolic Logic
- 2022

It is proved that T is interpretable in Q by producing a formal interpretation of T in an elementary concatenation theory QT+, thereby also establishing mutual interpretability of T with several well-known weak essentially undecidable theories of numbers, strings, and sets.

### Undecidability in First-Order Theories of Term Algebras Extended with a Substitution Operator

- Mathematics
- 2021

We introduce a first-order theory of finite full binary trees and then identify decidable and undecidable fragments of this theory. We show that the analogue of Hilbert‘s 10th Problem is undecidable…

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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…

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Q^- is a weaker variant of Robinson arithmetic Q in which addition and multiplication are partial functions, i.e. ternary relations that are graphs of possibly non-total functions. We show that Q is…

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We consider the problem stated by Andrzej Grzegorczyk in “Undecidability without arithmetization” (Studia Logica 79(2005)) whether certain weak theory of concatenation is essentially undecidable. We…

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First-order concatenation theory with bounded quantifiers is studied, axiomatizations with interesting properties are given, and a number of decidability and undecidability results are proved.

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