Asaf Karagila
I don't have much choice...

## The Axiom of Choice and Self-Dual Vector Spaces

I have uploaded a note titled The Axiom of Choice and Self-Duality of Vector Spaces. Here is a short summary and background.

It is a well known fact (in $$\ZFC$$ at least) that if $$V$$ is a vector space, and $$V^\ast$$ is the algebraic dual of $$V$$ then $$V\cong V^{\ast\ast}$$ if and only if $$\dim V<\infty$$.