The model theory of Commutative Near Vector Spaces
Logic
2022-07-12 v2
Abstract
In this paper we study near vector spaces over a commutative 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 are automorphisms of the near vector space.
Keywords
Cite
@article{arxiv.1807.06563,
title = {The model theory of Commutative Near Vector Spaces},
author = {Karin-Therese Howell and Charlotte Kestner},
journal= {arXiv preprint arXiv:1807.06563},
year = {2022}
}