Model-theory of vector-spaces over unspecified fields |
| |
Authors: | David Pierce |
| |
Institution: | (1) Mathematics Department, Middle East Technical University, 06531 Ankara, Turkey |
| |
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.
|
| |
Keywords: | Vector spaces Model-completeness Sort |
本文献已被 SpringerLink 等数据库收录! |
|