Subspaces of Computable Vector Spaces
Status: published in the Journal
of Algebra 314 (2007) 888 - 894.
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
over RCA0, and that the existence of a finite-dimensional nontrivial proper
subspace of such a vector space is equivalent to ACA0 over RCA0.