HEREDITARILY SEPARABLE GROUPS AND MONOCHROMATIC UNIFORMIZATION

We give a combinatorial equivalent to the existence of a non-free here ditarily separable group of cardinality aleph(1). This can be used, to gether with a known combinatorial equivalent of the existence of a non -free Whitehead group, to prove that it is consistent that every White head 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 pr imes is essential for this result.