### A characterization of ${\rm Ext}(G,{\mathbb Z})$ assuming $(V=L)$

by Shelah and Struengmann. [ShSm:873]

Fundamenta Math, 2007

In this paper we complete the characterization of Ext (G, Z)
under G{o}del's axiom of constructibility for
any torsion-free abelian group G . In particular, we prove in
(V=L) that, for a singular cardinal nu of uncountable
cofinality which is less than the first weakly compact cardinal and
for every sequence of cardinals (nu_p : p in Pi) satisfying
nu_p <= 2^{nu}, there is a torsion-free abelian group G of
size nu such that nu_p equals the p-rank of Ext (G,
Z) for every prime p and 2^{nu} is the torsion-free
rank of Ext (G, Z) .

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