In 1974, Shelah proved that Whitehead’s problem (a proposed characterization of free abelian groups) was not decidable in ZFC (the usual axioms of set theory, together with the axiom of choice). With his proof, powerful set-theoretic methods entered homological algebra. However, one might get the impression that set-theoretic methods are primarily useful for proving undecidability of mathematical problems.

The talk will demonstrate that set-theoretic methods can be employed in proving results in homological algebra that hold in ZFC and have strong consequences for the structure of representations of algebras, and modules in general.