We complete the characterization of Ext(G,ℤ) for any torsion-free abelian group G assuming Gödel’s axiom of constructibility plus there is no weakly compact cardinal. In particular, we prove in (V = L) that, for a singular cardinal ν of uncountable cofinality which is less than the first weakly compact cardinal and for every sequence of cardinals satisfying (where Π is the set of all primes), there is a torsion-free abelian group G of size ν such that equals the p-rank of Ext(G,ℤ) for every prime p and is the torsion-free rank of Ext(G,ℤ).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm193-2-3,
author = {Saharon Shelah and Lutz Str\"ungmann},
title = {A characterization of Ext(G,$\mathbb{Z}$) assuming (V = L)},
journal = {Fundamenta Mathematicae},
volume = {193},
year = {2007},
pages = {141-151},
zbl = {1116.20036},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm193-2-3}
}
Saharon Shelah; Lutz Strüngmann. A characterization of Ext(G,ℤ) assuming (V = L). Fundamenta Mathematicae, Tome 193 (2007) pp. 141-151. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm193-2-3/