Model-theory of vector-spaces over unspecified fields

Date

2009-06-01

Author

Pierce, David

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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.

Subject Keywords

Vector spaces, Model-completeness, Sort

URI

https://hdl.handle.net/11511/63860

Journal

ARCHIVE FOR MATHEMATICAL LOGIC

DOI

https://doi.org/10.1007/s00153-009-0130-x

Collections

Department of Mathematics, Article

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Citation Formats

D. Pierce, “Model-theory of vector-spaces over unspecified fields,” ARCHIVE FOR MATHEMATICAL LOGIC, pp. 421–436, 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63860.