##
Subspaces of Computable Vector Spaces

Status: published in the *Journal
of Algebra* 314 (2007) 888 - 894.

Availability: journal
version and preprint

**Abstract.** 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 WKL_{0}
over RCA_{0}, and that the existence of a finite-dimensional nontrivial proper
subspace of such a vector space is equivalent to ACA_{0} over RCA_{0}.

drh@math.uchicago.edu