The connection between ladder system uniformization and the Whitehead problem, part 1

We give a brief overview on what had been already known, and present our new result asserting that (appropriate) uniformization principles grant not only the existence of almost free but non-free Whitehead groups, but imply that each strongly $\aleph_1$ abelian group of power $\aleph_1$ has the Whitehead property. This is joint work with S. Shelah (paper #486 in Shelah's list).