The dual of an abelian group $A$ is defined to be the group $\text{Hom}(A,\mathbb Z)$ of homomorphisms to the infinite cyclic group. As usual with such dualities, there's a canonical homomorphism from $A$ to its double dual $$ A\to A^{**}:a\mapsto(h\mapsto h(a)). $$ If this is an isomorphism, $A$ is said to be reflexive.

Question: Are all free abelian groups reflexive?

Answer: Yes if and only if there are no measurable cardinals.