Hereditarily separable groups and monochromatic uniformization

2004/06/27 by Paul C. Eklof, Alan H. Mekler, Saharon Shelah
Mathematics · #math.LO #math.GR

paper · pdf

published as Israel Journal of Mathematics, 88:213-235, 1994

arxiv created 2004/06/27 · arxiv updated 2009/12/01

Abstract

We give a combinatorial equivalent to the existence of a non-free hereditarily separable group of cardinality aleph₁. 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.

Related

• New non-free Whitehead groups (corrected version)
• Filtration equivalent aleph₁-separable abelian groups of cardinality aleph₁
• Between Whitehead groups and uniformization
• Borel Whitehead groups
• The first almost free Whitehead group