On Monday, November 18, 2013 2:17:05 PM UTC-6, Sandy wrote: > Is it the case that > > > > a module has a basis iff it is a free module?
> Is it the case that > > > > (i) every vector space has a basis iff the axiom of choice holds;
> (ii) for every vector space V, > > (if B and C are bases of V then, there is a bijection: B -> C) > > iff the axiom of choice holds
I don't know for sure, but my dim memory is that this is strictly weaker than the full axiom of choice. You might want to check out the website/book on equivalents to the Axiom of Choice by the Rubins.