Ulm's Theorem presents invariants that classify countable abelian torsion
groups up to isomorphism. Barwise and Eklof extended this result to the
classification of arbitrary abelian torsion groups up to L∞ω-equivalence. In this paper, we extend this classification to a class
of mixed Zp-modules which includes all Warfield modules and is
closed under L∞ω-equivalence. The defining property of these
modules is the existence of what we call a partial decomposition basis, a
generalization of the concept of decomposition basis. We prove a complete
classification theorem in L∞ω using invariants deduced from the
classical Ulm and Warfield invariants