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arXiv · 2408.12883

There exists a d-minimal expansion of the $\mathbb R$-vector space over $\mathbb R$ which defines every sequence

Masato Fujita
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Abstract

There exists a d-minimal expansion of the $\mathbb R$-vector space over $\mathbb R$ which defines every sequence. In this paper, we prove this assertion and the following more general assertion: Let $\mathcal R$ be either the ordered $\mathbb R$-vector space structure over $\mathbb R$ or the ordered group of reals. A first-order expansion of $\mathcal R$ by a countable subset $D$ of $\mathbb R$ and a compact subset $E$ of $\mathbb R$ of finite Cantor-Bendixson rank is d-minimal if $(\mathcal R,D)$ is locally o-minimal.

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Masato Fujita. 2024-08-23. There exists a d-minimal expansion of the $\mathbb R$-vector space over $\mathbb R$ which defines every sequence. https://arxiv.org/abs/2408.12883

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