Geodesic
The $p$-rank of $\operatorname{Ext}_\mathbb Z(G,\mathbb Z)$ in certain models of~$ZFC$
Algebra i logika, Tome 46 (2007) no. 3, pp. 369-397.

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We prove that if the existence of a supercompact cardinal is consistent with $ZFC$, then it is consistent with $ZFC$ that the $p$-rank of $\operatorname{Ext}_\mathbb Z(G,\mathbb Z)$ is as large as possible for every prime $p$ and for any torsion-free Abelian group $G$. Moreover, given an uncountable strong limit cardinal $\mu$ of countable cofinality and a partition of $\Pi$ (the set of primes) into two disjoint subsets $\Pi_0$ and $\Pi_1$, we show that in some model which is very close to $ZFC$, there is an almost free Abelian group $G$ of size $2^\mu=\mu^+$ such that the $p$-rank of $\operatorname{Ext}_\mathbb Z(G,\mathbb Z)$ equals $2^\mu=\mu^+$ for every $p\in\Pi_0$ and 0 otherwise, that is, for $p\in\Pi_1$.
Keywords: theory $ZFC$, supercompact cardinal, strong limit cardinal, almost free Abelian group.
Mots-clés : torsion-free Abelian group 
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S. Shelah; L. Strüngmann. The $p$-rank of $\operatorname{Ext}_\mathbb Z(G,\mathbb Z)$ in certain models of~$ZFC$. Algebra i logika, Tome 46 (2007) no. 3, pp. 369-397. http://geodesic.mathdoc.fr/item/AL_2007_46_3_a5/

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