Homological Algebra and Set Theory
Paul C. Eklof · Transactions of the American Mathematical Society · 1977
Assuming the Axiom of Constructibility, necessary and sufficient conditions are given for the vanishing of ${\operatorname {Ext}}_\Lambda ^1$ for rings $\Lambda$ of global dimension 1. Using Martin’s Axiom, the necessity of these conditions is shown not to be a theorem of ZFC. Applications are given to abelian group theory, including a partial solution (assuming ${\text {V}} = {\text {L}}$) to a problem of Baer on the splitting of abelian groups. Some independence results in abelian group theory are also proved.