A characterization of Ext(G,Z) assuming V=L

Details A characterization of Ext(G,Z) assuming V=L A characterization of Ext(G,Z) assuming V=L

2006-09-22

arxiv.org/abs/math/0609638v1

Mathematics

Logic

Scientific paper

In this paper we complete the characterization of Ext(G,Z) under Godel'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 P) 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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