Generalizing a theorem of B\`{e}s and Choffrut

Erik Walsberg

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arXiv · 2002.10508

Generalizing a theorem of B\`{e}s and Choffrut

Erik Walsberg

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Abstract

B\`{e}s and Choffrut recently showed that there are no intermediate structures between $(\mathbb{R},<,+)$ and $(\mathbb{R},<,+,\mathbb{Z})$. We prove a generalization: if $\mathcal{R}$ is an o-minimal expansion of $(\mathbb{R},<,+)$ by bounded subsets of Euclidean space then there are no intermediate structures between $\mathcal{R}$ and $(\mathcal{R},\mathbb{Z})$. It follows there are no intermediate structures between $(\mathbb{R},<,+,\sin|_{[0,2\pi]})$ and $(\mathbb{R},<,+,\sin)$.

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BibTeX RIS

Erik Walsberg. 2020-02-24. Generalizing a theorem of B\`{e}s and Choffrut. https://arxiv.org/abs/2002.10508

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