Hereditarily separable groups and monochromatic uniformization
Paul C. Eklof, Alan H. Mekler, Saharon Shelah
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.
Create a lesson
Related papers
Pseudofinite abelian groups and asymptotic classes of finite abelian groups
Carlos Cordoba-Caycedo, Dario Garcia
Spectral Theory and Descriptive Combinatorics for Non-Regular Borel pmp Graphs
Cecelia Higgins, Pieter Spaas, Sofia Torelli
The strength of the minimum principle in constructive reverse mathematics
Tatsuji Kawai
Independence of premise for intuitionistic Zermelo-Fraenkel set theory
Patrick Uftring
Condensed Whitehead Problem
Spencer Unger, Jerry Wei
Points and their multiples on curves in powers of simple abelian varieties
David J. Smith