A simple proof for a theorem of Chase (Q1070041)

The author gives a new proof of the following well-known Theorem of Chase: Assume \(2^{\aleph_ 0}<2^{\aleph_ 1}\). If G is a torsion- free group such that Ext(G,Z) is torsion, then G is strongly \(\aleph_ 1\)-free. The idea of the proof is obvious for some one familiar with recent structure theorems of Ext, the solution of the Whitehead problem etc: Use the weak diamond (Devlin and Shelah) which follows from the set theoretic assumption. The smoothest way to prove Chase's theorem is then by Baer's factor systems.