Model-theory of vector-spaces over unspecified fields


Pierce D.

ARCHIVE FOR MATHEMATICAL LOGIC, vol.48, no.5, pp.421-436, 2009 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 48 Issue: 5
  • Publication Date: 2009
  • Doi Number: 10.1007/s00153-009-0130-x
  • Journal Name: ARCHIVE FOR MATHEMATICAL LOGIC
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.421-436

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.