2.4 (1966)

(S. Chase). Suppose that an abelian group $A$ can be written as the union of pure subgroups $A_\alpha$, $\alpha \in \Omega$, where $\Omega$ is the first non-denumerable ordinal, $A_\alpha$ is a free abelian group of denumerable rank, and, if $\beta < \alpha$, then $A_\beta$ is a direct summand of $A_\alpha$. Does it follow that $A$ is a free abelian group?