There is no maximal decidable expansion of the $\langle \mathbb{N} ,\{ < \} \rangle$ structure

Sergei Soprunov

There is no maximal decidable expansion of the $\langle \mathbb{N} ,\{ < \} \rangle$ structure

Logic 2022-11-30 v3

Authors: Sergei Soprunov

Abstract

We are going to prove that if the theory of a structure $\mathcal M=\langle \mathbb{N}, \Sigma \rangle$ is decidable and the standard order $<$ on natural numbers $\mathbb{N}$ is definable in $\mathcal M$ , then there is a nontrivial decidable expansion of $\mathcal M$

Cite

@article{arxiv.1911.09059,
  title  = {There is no maximal decidable expansion of the $\langle \mathbb{N} ,\{ < \} \rangle$ structure},
  author = {Sergei Soprunov},
  journal= {arXiv preprint arXiv:1911.09059},
  year   = {2022}
}

Comments

found an error in the proof of statement 2, page 3

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