Subspaces of Computable Vector Spaces

by Rod Downey, Denis R. Hirschfeldt, Asher M. Kach, Steffen Lempp, Joseph R. Mileti, and Antonio Montalbán

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 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.