Homological Algebra and Set Theory

Paul C. Eklof
1977 Transactions of the American Mathematical Society  
Assuming the Axiom of Constructibility, necessary and sufficient conditions are given for the vanishing of Ext\ for rings A 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 V = L) to a problem of Baer on the splitting of abelian groups. Some independence results in abelian group theory are also proved.
doi:10.2307/1997458 fatcat:zqegesbhvvhrpjspzkeqmen7ja