Simple product and locally o-minimal theories

2021/10/22 by Masato Fujita, Fujita, Masato
Computer Science · Mathematics · #03C64 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2110.11596

openalex publication_date 2021/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

There exist NIP and non-NTP₂ theories satisfying all the following conditions: It is not o-minimal; All models are strongly locally o-minimal; It has a model which is an expansion of the linearly ordered abelian group over the reals (\mathbb R ; 0,+,<). We construct these examples using the notion of simple product.

Citations

• Externally definable sets and dependent pairs

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