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Model-theory of vector-spaces over unspecified fields

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Abstract

Vector spaces over unspecified fields can be axiomatized as one-sorted structures, namely, abelian groups with the relation of parallelism. Parallelism is binary linear dependence. When equipped with the n-ary relation of linear dependence for some positive integer n, a vector-space is existentially closed if and only if it is n-dimensional over an algebraically closed field. In the signature with an n-ary predicate for linear dependence for each positive integer n, the theory of infinite-dimensional vector spaces over algebraically closed fields is the model-completion of the theory of vector spaces.

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  1. Mathematics Department, Middle East Technical University, 06531, Ankara, Turkey

    David Pierce

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  1. David Pierce
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Pierce, D. Model-theory of vector-spaces over unspecified fields. Arch. Math. Logic 48, 421–436 (2009). https://doi.org/10.1007/s00153-009-0130-x

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