2025/02/26 by Masato Fujita, Fujita, Masato · 1 citation
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Limits and Structures in Graph Theory #Logic (math.LO) #Primary 03C64 #Secondary 03C45
paper · pdf · doi:10.48550/arxiv.2502.18721
openalex publication_date 2025/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider an expansion \mathcal G=(G,<,+,…) of an ordered divisible Abelian group of finite burden defining no nonempty subset X of G which is dense and codense in a definable open subset U of G with X ⊆ U. We further assume that \mathcal G is nonvaluational, that is, for every nonempty definable subsets A,B of G with A<B and A ∪ B=G, inf\b-a | a ∈ A, b ∈ B\=0. Then, \mathcal G is *‑locally weakly o‑minimal. We also give a complete description of sets definable in a definably complete expansion of an ordered group of burden two if it defines an infinite discrete set.