This very nice paper deals with a version of the Whitehead problem under ZFC + GCH which also provides new results towards the existence of covers -- a topic in the center of research for the last decade in module theory: Assuming ZFC + GCH the authors show that it is consistent that for every Whitehead group \(A\) of infinite rank there is another one \(B\) with \(\text{Ext}(B,A)\neq 0\). Note that often it is equally hard to show non-splitting as splitting of short exact sequences. In this case \(A\) would ``like to split''. It follows (essentially rephrasing the last statement) the answer to an open problem for approximations of modules: Under the same set theoretic hypothesis it is undecidable whether every Abelian group has a \(^\bot\{\mathbb{Z}\}\)-precover. For many related results, also those concerning the existence of precovers we refer to the paper which is dedicated to the memory of Reinhold Baer.