Salce's problem on cotorsion pairs is undecidable
Logic
2022-01-11 v3 Commutative Algebra
Category Theory
Rings and Algebras
Representation Theory
Abstract
Salce \cite{MR565595} introduced the notion of a \emph{cotorsion pair} of classes of abelian groups, and asked whether every such pair is \emph{complete} (i.e., has enough injectives and projectives). We prove that it is consistent, relative to the consistency of Vop\v{e}nka's Principle (VP), that the answer is affirmative. Combined with a previous result of Eklof-Shelah \cite{MR2031314}, this shows that Salce's Problem is independent of the ZFC axioms (modulo the consistency of VP).
Cite
@article{arxiv.2103.06687,
title = {Salce's problem on cotorsion pairs is undecidable},
author = {Sean Cox},
journal= {arXiv preprint arXiv:2103.06687},
year = {2022}
}
Comments
To appear in Bulletin of the London Mathematical Society