The consistency of Ext(G,Z)=Q

For abelian groups, ifV=L, Ext(G, Z) cannot have cardinality ℵ₀. We show that G.C.H. does not imply this. See Hiller and Shelah 2], Hiller, Huber and Shelah 3], Nunke 5] and Shelah 6, 7, 8] for related results. We use the method of 7]. The author would like to thank the United States-Israel Binational Science Foundation for partially supporting this research by Grant No. 1110.