Test sets for factorization properties of modules

Baer's Criterion of injectivity implies that injectivity of a module is a factorization property with respect to a single monomorphism. Using the notion of a cotorsion pair, we study generalizations and dualizations of factorization properties in dependence on the algebraic structure of the underlying ring R and on additional set-theoretic hypotheses. For R commutative noetherian of Krull dimension 0 < d < infinity, we show that the assertion `projectivity is a factorization property with respect to a single epimorphism' is independent of ZFC + GCH. We also show that if R is any ring and there exists a strongly compact cardinal kappa > vertical bar R vertical bar, then the category of all projective modules is kappa-accessible.