Uniform Bounds in D-Minimal Structures
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866913180080406528 |
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| author | Farris, Madie Hieronymi, Philipp |
| author_facet | Farris, Madie Hieronymi, Philipp |
| contents | Let $\mathcal{R}$ be an expansion of the real field such that every subset of $\mathbb{R}$ definable in $\mathcal{R}$ either has interior or is a finite union of discrete sets. Answering a question by Chris Miller, we show that for every $n\in \mathbb{N}$ and every definable subset $A\subseteq \mathbb{R}^{n+1}$ there is $N\in \mathbb{N}$ such that for all $x\in \mathbb{R}^n$ either $A_x$ has interior or is the union of $N$ discrete sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_02316 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Uniform Bounds in D-Minimal Structures Farris, Madie Hieronymi, Philipp Logic Let $\mathcal{R}$ be an expansion of the real field such that every subset of $\mathbb{R}$ definable in $\mathcal{R}$ either has interior or is a finite union of discrete sets. Answering a question by Chris Miller, we show that for every $n\in \mathbb{N}$ and every definable subset $A\subseteq \mathbb{R}^{n+1}$ there is $N\in \mathbb{N}$ such that for all $x\in \mathbb{R}^n$ either $A_x$ has interior or is the union of $N$ discrete sets. |
| title | Uniform Bounds in D-Minimal Structures |
| topic | Logic |
| url | https://arxiv.org/abs/2606.02316 |