# 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. arXiv: math/0609638 DOI: 10.4064/fm193-2-3 MR: 2282712 -
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}). - 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} }