### Hereditarily separable groups and monochromatic uniformization

by Eklof and Mekler and Shelah. [EMSh:442]

Israel J Math, 1994

We give a combinatorial equivalent to the existence of a
non-free hereditarily separable group of cardinality aleph_1 . This
can be used, together with a known combinatorial equivalent of the
existence of a non-free Whitehead group, to prove that it is
consistent that every Whitehead group is free but not every
hereditarily separable group is free. We also show that the fact
that Z is a p.i.d. with infinitely many primes is
essential for this result.

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