Embedding Groups into the Baer-Specker Group

Moses Klein

A torsion-free abelian group is called countably separable if every countable subgroup is contained in a countable free direct summand. In 1989 Dugas and Irwin proved the following statement independent of ZF C: Every countably separable group is isomorphic to a pure subgroup of the Baer-Specker group Z^{ω}. Their proof used ⋄ and MA. We extend this result by showing that the statement is also independent of any axioms about cardinal exponentiation.

Address: Department of Mathematics, 480 Lincoln Dr., Madison, WI 53706, USA

E-mail: klein@math.wisc.edu