Hereditarily separable groups and monochromatic uniformization
Logic
2007-05-23 v1 Group Theory
Abstract
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.
Cite
@article{arxiv.math/0406552,
title = {Hereditarily separable groups and monochromatic uniformization},
author = {Paul C. Eklof and Alan H. Mekler and Saharon Shelah},
journal= {arXiv preprint arXiv:math/0406552},
year = {2007}
}