# Sh:874

- Shelah, S., & Strüngmann, L. H. (2007).
*On the p-rank of \mathrm{Ext}_{\mathbb Z}(G,\mathbb Z) in certain models of ZFC*. Algebra Logika,**46**(3), 369–397, 403–404. arXiv: math/0609637 DOI: 10.1007/s10469-007-0019-x MR: 2356727 -
Abstract:

We show that if the existence of a supercompact cardinal is consistent with ZFC, then it is consistent with ZFC that the p-rank of {\rm Ext}_{\mathbb Z}(G,\mathbb Z) is as large as possible for every prime p and any torsion-free abelian group G. Moreover, given an uncountable strong limit cardinal \mu of countable cofinality and a partition of \Pi (the set of primes) into two disjoint subsets \Pi_0 and \Pi_1, we show that in some model which is very close to ZFC there is an almost-free abelian group G of size 2^{\mu}=\mu^+ such that the p-rank of {\rm Ext}_{\mathbb Z}(G,{\mathbb Z}) equals 2^{\mu}=\mu^+ for every p\in\Pi_0 and 0 otherwise, i.e. for p\in\Pi_1. - Version 2006-01-11_11 (21p) published version (16p)

Bib entry

@article{Sh:874, author = {Shelah, Saharon and Str{\"u}ngmann, Lutz H.}, title = {{On the $p$-rank of $\mathrm{Ext}_{\mathbb Z}(G,\mathbb Z)$ in certain models of ZFC}}, journal = {Algebra Logika}, fjournal = {Algebra i Logika. Institut Diskretno\u{\i} Matematiki i Informatiki}, volume = {46}, number = {3}, year = {2007}, pages = {369--397, 403--404}, issn = {0373-9252}, mrnumber = {2356727}, mrclass = {03E75 (20K20 20K35)}, doi = {10.1007/s10469-007-0019-x}, note = {\href{https://arxiv.org/abs/math/0609637}{arXiv: math/0609637}}, arxiv_number = {math/0609637} }