7 papers
Hereditarily separable groups and monochromatic uniformization
Paul C. Eklof, Alan H. Mekler, Saharon Shelah
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 equival…
On the cogeneration of cotorsion pairs
Paul C. Eklof, Saharon Shelah, Jan Trlifaj
Let R be a Dedekind domain. Enochs' solution of the Flat Cover Conjecture was extended as follows: (*) If C is a cotorsion pair generated by a class of cotorsion modules, then C is…
The structure of Ext(A,Z) and GCH: possible co-Moore spaces
Paul C. Eklof, Saharon Shelah
We consider what Ext(A,Z) can be when A is torsion-free and Hom(A,Z)=0. We thereby give an answer to a question of Golasinski and Goncalves which asks for the divisible Abelian gro…
Whitehead modules over large principal ideal domains
Paul C. Eklof, Saharon Shelah
We consider the Whitehead problem for principal ideal domains of large size. It is proved, in ZFC, that some p.i.d.'s of size >= aleph_{2} have non-free Whitehead modules even thou…
On Whitehead precovers
Paul C. Eklof, Saharon Shelah
It is proved undecidable in ZFC + GCH whether every Z-module has a^{perp} {Z}-precover.
Absolutely rigid systems and absolutely indecomposable groups
Paul C. Eklof, Saharon Shelah
We give a new proof that there are arbitrarily large indecomposable abelian groups; moreover, the groups constructed are absolutely indecomposable, that is, they remain indecomposa…