The model theory of Commutative Near Vector Spaces

2018/07/17 by Karin-Therese Howell, Howell, Karin-Therese, Charlotte Kestner +1
Mathematics · #Advanced Banach Space Theory #Advanced Topics in Algebra #FOS: Mathematics #Logic (math.LO) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1807.06563

openalex publication_date 2018/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study near vector spaces over a commutative F from a model theoretic point of view. In this context we show regular near vector spaces are in fact vector spaces. We find that near vector spaces are not first order axiomatisable, but that finite block near vector spaces are. In the latter case we establish quantifier elimination, and that the theory is controlled by which elements of the pointwise additive closure of F are automorphisms of the near vector space.

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