Abstract:
The notions of linear and metric independence are investigated in relation to the property: if U is a set of m + 1 independent vectors,
and X is a set of m independent vectors, then adjoining some vector in U to
X results in a set of m + 1 independent vectors. A weak countable choice axiom is introduced, in the presence of which linear and metric independence are
equivalent. Proofs are carried out in the context of intuitionistic logic.