Submission date: 17 July 2018

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.

Mathematics Subject Classification:

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Full text arXiv 1807.06563: pdf, ps.