2024/08/23 by Masato Fujita, Fujita, Masato
Mathematics · #03C64 #Advanced Banach Space Theory #Advanced Topology and Set Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.2408.12883
openalex publication_date 2024/08/23 · openalex created_date 2024/10/21 · openalex updated_date 2026/07/28
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.