# Sh:873

• Shelah, S., & Strüngmann, L. H. (2007). A characterization of \mathrm{Ext}(G,\mathbb Z) assuming (V=L). Fund. Math., 193(2), 141–151.
• Abstract:
In this paper we complete the characterization of {\rm Ext}(G,{\mathbb Z}) under Gödel’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 \leq 2^{\nu}, there is a torsion-free abelian group G of size \nu such that \nu_p equals the p-rank of {\rm Ext}(G, {\mathbb Z}) for every prime p and 2^{\nu} is the torsion-free rank of {\rm Ext}(G,{\mathbb Z}).
• Current version: 2006-09-19_11 (9p) published version (11p)
Bib entry
@article{Sh:873,
author = {Shelah, Saharon and Str{\"u}ngmann, Lutz H.},
title = {{A characterization of $\mathrm{Ext}(G,\mathbb Z)$ assuming $(V=L)$}},
journal = {Fund. Math.},
fjournal = {Fundamenta Mathematicae},
volume = {193},
number = {2},
year = {2007},
pages = {141--151},
issn = {0016-2736},
mrnumber = {2282712},
mrclass = {20K15 (20K20 20K40)},
doi = {10.4064/fm193-2-3},
note = {\href{https://arxiv.org/abs/math/0609638}{arXiv: math/0609638}},
arxiv_number = {math/0609638}
}