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Homological Algebra and Set Theory
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