Shelah's singular compactness theorem is a general result showing that a singular cardinal λ has properties reminiscent of those enjoyed by large cardinals: for example

• If G is an abelian group of size λ and every subgroup of G with size less than λ is free, then G is free.
• If X is a family of size λ of countable sets, and every subfamily of size less than λ has a transversal, then X has a transversal.