Subspaces of Computable Vector Spaces

@inproceedings{Downey2006SubspacesOC,
  title={Subspaces of Computable Vector Spaces},
  author={Rodney G. Downey and Denis R. Hirschfeldt and Asher M. Kach and Steffen Lempp and Joseph R. Mileti and Antonio Montalb{\'a}n},
  year={2006}
}
We show that the existence of a nontrivial proper subspace of a vector space of dimension greater than one (over an infinite field) is equivalent to WKL0 over RCA0, and that the existence of a finite-dimensional nontrivial proper subspace of such a vector space is equivalent to ACA0 over RCA0. 

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