A characterization of $\mathop{\rm Ext}(G,\mathbb Z)$ assuming $(V=L)$
Volume 193 / 2007
Fundamenta Mathematicae 193 (2007), 141-151
MSC: Primary 20K15, 20K20,
20K35, 20K40; Secondary 18E99, 20J05.
DOI: 10.4064/fm193-2-3
Abstract
We complete the characterization of $\mathop{\rm Ext}(G,\mathbb Z)$ 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 $\nu$ of uncountable cofinality which is less than the first weakly compact cardinal and for every sequence $( \nu_p : p \in \varPi )$ of cardinals satisfying $\nu_p \leq 2^{\nu}$ (where $\varPi$ is the set of all primes), there is a torsion-free abelian group $G$ of size $\nu$ such that $\nu_p$ equals the $p$-rank of $\mathop{\rm Ext}(G,\mathbb Z)$ for every prime $p$ and $2^{\nu}$ is the torsion-free rank of $\mathop{\rm Ext}(G,\mathbb Z)$.
