• DOI:10.1007/978-3-030-51466-2_6
• Corpus ID: 220042713

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}
}

• L. Kristiansen, Juvenal Murwanashyaka
• Published 24 June 2020
• Materials Science
• Beyond the Horizon of Computability

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{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {T}$$\end{document}. The intended model for the theories is a term model. We prove that \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} is mutually interpretable with Robinson’s \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {R}$$\end{document}. Moreover, we prove that Robinson’s \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {Q}$$\end{document} is interpretable in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {T}$$\end{document}.