Model-theory of vector-spaces over unspecified fields


Pierce D.

ARCHIVE FOR MATHEMATICAL LOGIC, cilt.48, ss.421-436, 2009 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 48 Konu: 5
  • Basım Tarihi: 2009
  • Doi Numarası: 10.1007/s00153-009-0130-x
  • Dergi Adı: ARCHIVE FOR MATHEMATICAL LOGIC
  • Sayfa Sayıları: ss.421-436

Özet

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.