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

Sergei Soprunov

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arXiv · 1911.09059

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

Sergei Soprunov

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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 $\mathcal M$

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BibTeX RIS

Sergei Soprunov. 2019-11-20. There is no maximal decidable expansion of the $\langle \mathbb{N} ,\{ < \} \rangle$ structure. https://arxiv.org/abs/1911.09059

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