  We discuss the lattice of cotorsion theories for abelian groups. First we
show that the sublattice of the well-studied rational cotorsion theories can be
identified with the well-known lattice of types. Using a recently developed
method for making Ext vanish we also prove that any power set together with the
ordinary set inclusion (and thus any poset) can be embedded into the lattice of
all cotorsion theories.
