论文标题
概括Bès和Choffrut定理
Generalizing a theorem of Bès and Choffrut
论文作者
论文摘要
Bès和Choffrut最近表明，$（\ Mathbb {r}，<，+）$和$（\ Mathbb {r}，<，+，\ Mathbb {z}）$之间没有中间结构。我们证明了一个概括：如果$ \ Mathcal {r} $是$（\ Mathbb {r}，<，+）$的o-sinimal扩展，则是欧几里得空间的有界子集，那么$ \ \ \ \ \ \ m natercal {r} $ and $（\ nathcal and $ nathcal and $ nathcal {\ mathcal {r mathbb} $}它遵循$（\ mathbb {r}，<，+，\ sin | _ {[0,2π]}）$和$（\ Mathbb {r}，<，+，\ sin）$之间的中间结构。
Bès 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 $(\mathbb{R},<,+,\sin|_{[0,2π]})$ and $(\mathbb{R},<,+,\sin)$.
